Physics

John D. Cutnell, Kenneth W. Johnson

Chapter 12

Temperature and Heat - all with Video Answers

Educators

Chapter Questions

Problem 1

A temperature of absolute zero occurs at $-273.15^{\circ} \mathrm{C}$. What is this temperature on the Fahrenheit scale?

Shahab Ullah

Shahab Ullah

Numerade Educator

Problem 2

Suppose you are hiking down the Grand Canyon. At the top, the temperature early in the morning is a $\operatorname{cool} 3^{\circ} \mathrm{C}$. By late afternoon, the temperature at the bottom of the canyon has warmed to a sweltering $34^{\circ} \mathrm{C}$. What is the difference between the higher and lower temperatures in (a) Fahrenheit degrees and (b) kelvins?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 3

On the moon the surface temperature ranges from $375 \mathrm{~K}$ during the day to $1.00 \times 10^{2} \mathrm{~K}$ at night. What are these temperatures on the (a) Celsius and (b) Fahrenheit scales?

Sanjeev Kumar

Numerade Educator

Problem 4

Dermatologists often remove small precancerous skin lesions by freezing them quickly with liquid nitrogen, which has a temperature of $77 \mathrm{~K}$. What is this temperature on the (a) Celsius and (b) Fahrenheit scales?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 5

What's your normal body temperature? It may not be $98.6^{\circ} \mathrm{F}$, the oft-quoted average that was determined in the nineteenth century. A more recent study has reported an average temperature of $98.2^{\circ} \mathrm{F}$. What is the difference between these averages, expressed in Celsius degrees?

Shahab Ullah

Numerade Educator

Problem 6

Space invaders land on earth. On the invaders' temperature scale, the ice point is at $25^{\circ} \mathrm{I}$ (I = invader), and the steam point is at $156^{\circ} \mathrm{I}$. The invaders' thermometer shows the temperature on earth to be $58^{\circ}$ I. Using logic similar to that in Example 1 in the text, what would this temperature be on the Celsius scale?

Shahab Ullah

Numerade Educator

Problem 6

Space invaders land on earth. On the invaders' temperature scale, the ice point is at $25^{\circ} \mathrm{I}$ (I = invader), and the steam point is at $156^{\circ} \mathrm{I}$. The invaders' thermometer shows the temperature on earth to be $58^{\circ}$ I. Using logic similar to that in Example 1 in the text, what would this temperature be on the Celsius scale?

Shahab Ullah

Numerade Educator

Problem 7

A constant-volume gas thermometer (see Figures $12-3$ and $12-4$ ) has a pressure of $5.00 \times 10^{3} \mathrm{~Pa}$ when the gas temperature is $0.00{ }^{\circ} \mathrm{C}$. What is the temperature $\left(\right.$ in $\left.{ }^{\circ} \mathrm{C}\right)$ when the pressure is $2.00 \times 10^{3} \mathrm{~Pa}$ ?

Narayan Hari

Numerade Educator

Problem 8

On the Rankine temperature scale, which is sometimes used in engineering applications, the ice point is at $491.67^{\circ} \mathrm{R}$ and the steam point is at $671.67^{\circ} \mathrm{R}$. Determine a relationship (analogous to Equation 12.1 ) between the Rankine and Fahrenheit temperature scales.

Narayan Hari

Numerade Educator

Problem 9

A steel section of the Alaskan pipeline had a length of $65 \mathrm{~m}$ and a temperature of $18^{\circ} \mathrm{C}$ when it was installed. What is its change in length when the temperature drops to a frigid $-45^{\circ} \mathrm{C} ?$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 10

An aluminum baseball bat has a length of $0.86 \mathrm{~m}$ at a temperature of $17^{\circ} \mathrm{C}$. When the temperature of the bat is raised, the bat lengthens by $0.00016 \mathrm{~m}$. Determine the final temperature of the bat.

Sanjeev Kumar

Numerade Educator

Problem 11

ssm www Find the approximate length of the Golden Gate bridge if it is known that the steel in the roadbed expands by $0.53 \mathrm{~m}$ when the temperature changes from +2 to $+32{ }^{\circ} \mathrm{C}$.

Narayan Hari

Numerade Educator

Problem 12

Conceptual Example 5 provides background for this problem. A hole is drilled through a copper plate whose temperature is $11{ }^{\circ} \mathrm{C}$. (a) When the temperature of the plate is increased, will the radius of the hole be larger or smaller than the radius at $11^{\circ} \mathrm{C}$ ? Why?
(b) When the plate is heated to $110^{\circ} \mathrm{C}$, by what fraction $\Delta r / r_{0}$ will the radius of the hole change?

Sanjeev Kumar

Numerade Educator

Problem 13

A steel beam is used in the construction of a skyscraper. By what fraction $\Delta L / L_{0}$ does the length of the beam increase when the temperature changes from that on a cold winter day $\left(-15^{\circ} \mathrm{F}\right)$ to that on a summer day $\left(+105^{\circ} \mathrm{F}\right) ?$

Narayan Hari

Numerade Educator

Problem 14

When the temperature of a coin is raised by $75 \mathrm{C}^{\circ},$ the coin's diameter increases by $2.3 \times 10^{-5} \mathrm{~m}$. If the original diameter of the coin is $1.8 \times 10^{-2} \mathrm{~m}$, find the coefficient of linear expansion.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 15

A rod made from a particular alloy is heated from $25.0^{\circ} \mathrm{C}$ to the boiling point of water. Its length increases by $8.47 \times 10^{-4} \mathrm{~m}$. The rod is then cooled from $25.0^{\circ} \mathrm{C}$ to the freezing point of water. By how much does the rod shrink?

Narayan Hari

Numerade Educator

Problem 16

Concrete sidewalks are always laid in sections, with gaps between each section. For example, the drawing shows three identical 2.4 -m sections, the outer two of which are against immovable walls. The two identical gaps between the sections are provided so that thermal expansion will not create the thermal stress that could lead to cracks. What is the minimum gap width necessary to account for an increase in temperature of $32 \mathrm{C}^{\circ} ?$

Sanjeev Kumar

Numerade Educator

Problem 17

The brass bar and the aluminum bar in the drawing are each attached to an immovable wall. At $28^{\circ} \mathrm{C}$ the air gap between the rods is $1.3 \times 10^{-3} \mathrm{~m}$. At what temperature will the gap be closed?

Sanjeev Kumar

Numerade Educator

Problem 18

Multiple-Concept Example 4 reviews the concepts that are involved in this problem. A ruler is accurate when the temperature is $25^{\circ} \mathrm{C}$. When the temperature drops to $-14^{\circ} \mathrm{C}$, the ruler shrinks and no longer measures distances accurately. However, the ruler can be made to read correctly if a force of magnitude $1.2 \times 10^{3} \mathrm{~N}$ is applied to each end so as to stretch it back to its original length. The ruler has a cross-sectional area of $1.6 \times 10^{-5} \mathrm{~m}^{2},$ and it is made from a material whose coefficient of linear expansion is $2.5 \times 10^{-5}\left(\mathrm{C}^{0}\right)^{-1}$. What is Young's modulus for the material from which the ruler is made?

Satpal Satpal

Numerade Educator

Problem 19

A simple pendulum consists of a ball connected to one end of a thin brass wire. The period of the pendulum is $2.0000 \mathrm{~s}$. The temperature rises by $140 \mathrm{C}^{\circ}$, and the length of the wire increases. Determine the period of the heated pendulum.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 20

As the drawing shows, two thin strips of metal are bolted together at one end and have the same temperature. One is steel, and the other is aluminum. The steel strip is $0.10 \%$ longer than the aluminum strip. By how much should the temperature of the strips be increased, so that the strips have the same length?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 21

Consult Conceptual Example 5 for background pertinent to this problem. A lead sphere has a diameter that is $0.050 \%$ larger than the inner diameter of a steel ring when each has a temperature of $70.0^{\circ} \mathrm{C}$. Thus, the ring will not slip over the sphere. At what common temperature will the ring just slip over the sphere?

Satpal Satpal

Numerade Educator

Problem 22

A steel bicycle wheel (without the rubber tire) is rotating freely with an angular speed of $18.00 \mathrm{rad} / \mathrm{s}$. The temperature of the wheel changes from -100.0 to $+300.0{ }^{\circ} \mathrm{C}$. No net external torque acts on the wheel, and the mass of the spokes is negligible. (a) Does the angular speed increase or decrease as the wheel heats up? Why? (b) What is the angular speed at the higher temperature?

Mayukh Banik

Numerade Educator

Problem 23

ssm A wire is made by attaching two segments together, end to end. One segment is made of aluminum and the other is steel. The effective coefficient of linear expansion of the two-segment wire is $19 \times 10^{-6}\left(\mathrm{C}^{\circ}\right)^{-1}$. What fraction of the length is aluminum?

Satpal Satpal

Numerade Educator

Problem 24

Consult Multiple-Concept Example 4 for insight into solving this problem. An aluminum wire of radius $3.0 \times 10^{-4} \mathrm{~m}$ is stretched between the ends of a concrete block, as the drawing illustrates. When the system (wire and concrete) is at $35^{\circ} \mathrm{C},$ the tension in the wire is $50.0 \mathrm{~N}$. What is the tension in the wire when the system is heated to $185{ }^{\circ} \mathrm{C} ?$

Satpal Satpal

Numerade Educator

Problem 25

A copper kettle contains water at $24^{\circ} \mathrm{C}$. When the water is heated to its boiling point, the volume of the kettle expands by $1.2 \times 10^{-5} \mathrm{~m}^{3}$. Determine the volume of the kettle at $24^{\circ} \mathrm{C}$.

Narayan Hari

Numerade Educator

Problem 26

A flask is filled with $1.500 \mathrm{~L}(\mathrm{~L}=$ liter $)$ of a liquid at $97.1{ }^{\circ} \mathrm{C}$. When the liquid is cooled to $15.0^{\circ} \mathrm{C}$, its volume is only $1.383 \mathrm{~L}$, however. Neglect the contraction of the flask and use Table $12-1$ to identify the liquid.

Narayan Hari

Numerade Educator

Problem 27

Interactive Solution 12.27 at presents a model for solving problems of this type. A thin spherical shell of silver has an inner radius of $2.0 \times 10^{-2} \mathrm{~m}$ when the temperature is $18^{\circ}$
C. The shell is heated to $147^{\circ} \mathrm{C}$. Find the change in the interior volume of the shell.

Narayan Hari

Numerade Educator

Problem 28

At a temperature of $0^{\circ} \mathrm{C}$, the mass and volume of a fluid are $825 \mathrm{~kg}$ and $1.17 \mathrm{~m}^{3}$. The coefficient of volume expansion is $1.26 \times 10^{-3}\left(\mathrm{C}^{\circ}\right)^{-1}$
(a) What is the density of the fluid at this temperature? (b) What is the density of the fluid when the temperature has risen to $20.0^{\circ} \mathrm{C} ?$

Satpal Satpal

Numerade Educator

Problem 29

A lead object and a quartz object each have the same initial volume. The volume of each increases by the same amount, because the temperature increases. If the temperature of the lead object increases by $4.0 \mathrm{C}^{\circ},$ by how much does the temperature of the quartz object increase?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 30

Consult Interactive LearningWare 12.1 at for help in solving this problem. During an all-night cram session, a student heats up a one-half liter $\left(0.50 \times 10^{-3} \mathrm{~m}^{3}\right)$ glass (Pyrex) beaker of cold coffee. Initially, the temperature is $18^{\circ} \mathrm{C},$ and the beaker is filled to the brim. A short time later when the student returns, the temperature has risen to $92^{\circ} \mathrm{C}$. The coefficient of volume expansion of coffee is the same as that of water. How much coffee (in cubic meters) has spilled out of the beaker?

Satpal Satpal

Numerade Educator

Problem 30

Consult Interactive LearningWare 12.1 at for help in solving this problem. During an all-night cram session, a student heats up a one-half liter $\left(0.50 \times 10^{-3} \mathrm{~m}^{3}\right)$ glass (Pyrex) beaker of cold coffee. Initially, the temperature is $18^{\circ} \mathrm{C},$ and the beaker is filled to the brim. A short time later when the student returns, the temperature has risen to $92^{\circ} \mathrm{C}$. The coefficient of volume expansion of coffee is the same as that of water. How much coffee (in cubic meters) has spilled out of the beaker?

Satpal Satpal

Numerade Educator

Problem 31

Suppose that the steel gas tank in your car is completely filled when the temperature is $17^{\circ} \mathrm{C}$. How many gallons will spill out of the twenty-gallon tank when the temperature rises to $35^{\circ} \mathrm{C} ?$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 32

Interactive LearningWare 12.1 at provides some useful background for this problem. Many hot-water heating systems have a reservoir tank connected directly to the pipeline, so as to allow for expansion when the water becomes hot. The heating system of a house has $76 \mathrm{~m}$ of copper pipe whose inside radius is $9.5 \times 10^{-3} \mathrm{~m}$. When the water and pipe are heated from 24 to $78{ }^{\circ} \mathrm{C}$, what must be the minimum volume of the reservoir tank to hold the overflow of water?

Narayan Hari

Numerade Educator

Problem 33

At the bottom of an old mercury-in-glass thermometer is a $45-\mathrm{mm}^{3}$ reservoir filled with mercury. When the thermometer was placed under your tongue, the warmed mercury would expand into a very narrow cylindrical channel, called a capillary, whose radius was $1.7 \times 10^{-2} \mathrm{~mm}$. Marks were placed along the capillary that indicated the temperature. Ignore the thermal expansion of the glass and determine how far (in $\mathrm{mm}$ ) the mercury would expand into the capillary when the temperature changed by $1.0 \mathrm{C}^{\circ}$.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 34

A solid aluminum sphere has a radius of $0.50 \mathrm{~m}$ and a temperature of $75^{\circ} \mathrm{C}$. The sphere is then completely immersed in a pool of water whose temperature is $25^{\circ} \mathrm{C}$. The sphere cools, while the water temperature remains nearly at $25^{\circ} \mathrm{C}$, because the pool is very large. The sphere is weighed in the water immediately after being submerged (before it begins to cool) and then again after cooling to $25^{\circ} \mathrm{C}$. (a) Which weight is larger? Why?
(b) Use Archimedes' principle to find the magnitude of the difference between the weights.

Satpal Satpal

Numerade Educator

Problem 35

The bulk modulus of water is $B=2.2 \times 10^{9} \mathrm{~N} / \mathrm{m}^{2}$. What change in pressure $\Delta P$ (in atmospheres) is required to keep water from expanding when it is heated from 15 to $25^{\circ} \mathrm{C} ?$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 36

A spherical brass shell has an interior volume of $1.60 \times 10^{-3} \mathrm{~m}^{3}$. Within this interior volume is a solid steel ball that has a volume of $0.70 \times 10^{-3} \mathrm{~m}^{3}$. The space between the steel ball and the inner surface of the brass shell is filled completely with mercury. A small hole is drilled through the brass, and the temperature of the arrangement is increased by $12 \mathrm{C}^{\circ} .$ What is the volume of the mercury that spills out of the hole?

Sanjeev Kumar

Numerade Educator

Problem 37

Two identical thermometers made of Pyrex glass contain, respectively, identical volumes of mercury and methyl alcohol. If the expansion of the glass is taken into account, how many times greater is the distance between the degree marks on the methyl alcohol thermometer than that on the mercury thermometer?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 38

The column of mercury in a barometer (see Figure $12-12$ ) has a height of $0.760 \mathrm{~m}$ when the pressure is one atmosphere and the temperature is $0.0^{\circ} \mathrm{C}$. Ignoring any change in the glass containing the mercury, what will be the height of the mercury column for the same one atmosphere of pressure when the temperature rises to $38.0^{\circ} \mathrm{C}$ on a hot day? (Hint:
The pressure in the barometer is given by Pressure $=\rho g h,$ and the density $\rho$ of the mercury changes when the temperature changes.)

Mayukh Banik

Numerade Educator

Problem 39

If the price of electrical energy is $\$ 0.10$ per kilowatt c hour, what is the cost of using electrical energy to heat the water in a swimming pool $(12.0 \mathrm{~m} \times 9.00 \mathrm{~m} \times 1.5 \mathrm{~m})$ from 15 to $27^{\circ} \mathrm{C} ?$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 40

When you take a bath, how many kilograms of hot water $\left(49.0^{\circ} \mathrm{C}\right)$ must you mix with cold water $\left(13.0^{\circ} \mathrm{C}\right)$ so that the temperature of the bath is $36.0^{\circ} \mathrm{C} ?$ The total mass of water (hot plus cold) is $191 \mathrm{~kg}$. Ignore any heat flow between the water and its external surroundings.

Satpal Satpal

Numerade Educator

Problem 41

Blood can carry excess energy from the interior to the surface of the body, where the energy is dispersed in a number of ways. While a person is exercising, $0.6 \mathrm{~kg}$ of blood flows to the surface of the body and releases $2000 \mathrm{~J}$ of energy. The blood arriving at the surface has the temperature of the body interior, $37.0^{\circ} \mathrm{C}$. Assuming that blood has the same specific heat capacity as water, determine the temperature of the blood that leaves the surface and returns to the interior.

Narayan Hari

Numerade Educator

Problem 42

An ice chest at a beach party contains 12 cans of soda at $5.0^{\circ} \mathrm{C}$. Each can of soda has a mass of $0.35 \mathrm{~kg}$ and a specific heat capacity of $3800 \mathrm{~J} /\left(\mathrm{kg} \cdot \mathrm{C}^{\circ}\right)$. Someone adds a $6.5-\mathrm{kg}$ watermelon at $27{ }^{\circ} \mathrm{C}$ to the chest. The specific heat capacity of watermelon is nearly the same as that of water. Ignore the specific heat capacity of the chest and determine the final temperature $T$ of the soda and watermelon.

Sanjeev Kumar

Numerade Educator

Problem 43

Review Interactive Solution $\underline{12.43}$ at for help in approaching this problem. When resting, a person has a metabolic rate of about $3.0 \times 10^{5}$ joules per hour. The person is submerged neck-deep into a tub containing $1.2 \times 10^{3} \mathrm{~kg}$ of water at $21.00{ }^{\circ} \mathrm{C}$. If the heat from the person goes only into the water, find the water temperature after half an hour.

Narayan Hari

Numerade Educator

Problem 44

A piece of glass has a temperature of $83.0^{\circ} \mathrm{C}$. Liquid that has a temperature of $43.0^{\circ} \mathrm{C}$ is poured over the glass, completely covering it, and the temperature at equilibrium is $53.0^{\circ}$
C. The mass of the glass and the liquid is the same. Ignoring the container that holds the glass and liquid and assuming that the heat lost to or gained from the surroundings is negligible, determine the specific heat capacity of the liquid.

Vinnu M

Numerade Educator

Problem 45

At a fabrication plant, a hot metal forging has a mass of $75 \mathrm{~kg}$ and a specific heat capacity of $430 \mathrm{~J} /\left(\mathrm{kg} \cdot \mathrm{C}^{\circ}\right) .$ To harden it, the forging is immersed in $710 \mathrm{~kg}$ of oil that has a temperature of $32^{\circ} \mathrm{C}$ and a specific heat capacity of $2700 \mathrm{~J} /\left(\mathrm{kg} \dot{\mathrm{c}} \mathrm{C}^{\circ}\right) .$ The final temperature of the oil and forging at thermal equilibrium is $47^{\circ} \mathrm{C}$. Assuming that heat flows only between the forging and the oil, determine the initial temperature of the forging.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 45

Multiple-Concept Example 11 deals with a situation that is similar, but not identical, to that here. When $4200 \mathrm{~J}$ of heat are added to a $0.15-\mathrm{m}$ -long silver bar, its length increases by $4.3 \times 10^{-3} \mathrm{~m}$. What is the mass of the bar?

Sanjeev Kumar

Numerade Educator

Problem 47

Interactive Solution 12.47 at deals with one approach to solving problems such as this. A $0.35-\mathrm{kg}$ coffee mug is made from a material that has a specific heat capacity of $920 \mathrm{~J} /$ $\left(\mathrm{kg} \cdot \mathrm{C}^{\circ}\right)$ and contains $0.25 \mathrm{~kg}$ of water. The cup and water are at $15^{\circ} \mathrm{C} .$ To make a cup of coffeee, a small electric heater is immersed in the water and brings it to a boil in three minutes. Assume that the cup and water always have the same temperature and determine the minimum power rating of this heater.

Narayan Hari

Numerade Educator

Problem 48

Multiple-Concept Example 11 uses the same physics principles as those employed in this problem. A block of material has a mass of $130 \mathrm{~kg}$ and a volume of $4.6 \times 10^{-2} \mathrm{~m}^{3} .$ The material has a specific heat capacity and coefficient of volume expansion, respectively, of $750 \mathrm{~J} /\left(\mathrm{kg} \cdot \mathrm{C}^{\circ}\right)$ and $4.6 \times 10^{5}\left(\mathrm{C}^{\circ}\right)^{-1}$. How much heat must be added to the block in order to increase its volume by $1.2 \times 10^{-5} \mathrm{~m}^{3}$ ?

Narayan Hari

Numerade Educator

Problem 49

An electric hot water heater takes in cold water at $13.0^{\circ} \mathrm{C}$ and delivers hot water. The hot water has a constant temperature of $45.0^{\circ} \mathrm{C}$ when the "hot" faucet is left open all the time, and the volume flow rate is $5.0 \times 10^{-6} \mathrm{~m}^{3 / \mathrm{s}}$. What is the minimum power rating of the hot water heater?

Narayan Hari

Numerade Educator

Problem 50

A $1.5-\mathrm{kg}$ steel sphere will not fit through a circular hole in a $0.85-\mathrm{kg}$ aluminum plate, because the radius of the sphere is $0.10 \%$ larger than the radius of the hole. If both the sphere and the plate are always kept at the same temperature, how much heat must be put into the two so the ball just passes through the hole?

Ummatul Choudary

Ummatul Choudary

Numerade Educator

Problem 51

How much heat must be added to $0.45 \mathrm{~kg}$ of aluminum to change it from a solid at $130{ }^{\circ} \mathrm{C}$ to a liquid at $660{ }^{\circ} \mathrm{C}$ (its melting point)? The latent heat of fusion for aluminum is $4.6 \times 10^{5} \mathrm{~J} / \mathrm{kg}$.

Narayan Hari

Numerade Educator

Problem 52

To help prevent frost damage, fruit growers sometimes protect their crop by spraying it with water when overnight temperatures are expected to go below the freezing mark. When the water turns to ice during the night, heat is released into the plants, thereby giving them a measure of protection against the falling temperature. Suppose a grower sprays $7.2 \mathrm{~kg}$ of water at $0^{\circ} \mathrm{C}$ onto a fruit tree. (a) How much heat is released by the water when it freezes? (b) How much would the temperature of a $180-\mathrm{kg}$ tree rise if it absorbed the heat released in part (a)? Assume that the specific heat capacity of the tree is $2.5 \times 10^{3} \mathrm{~J} /\left(\mathrm{kg} \cdot \mathrm{C}^{\circ}\right)$ and that no phase change occurs within the tree itself.

Satpal Satpal

Numerade Educator

Problem 53

Assume that the pressure is one atmosphere and determine the heat required to produce $2.00 \mathrm{~kg}$ of water vapor at $100.0^{\circ} \mathrm{C}$, starting with (a) $2.00 \mathrm{~kg}$ of water at $100.0^{\circ} \mathrm{C}$ and ( $\mathrm{b}$ ) $2.00 \mathrm{~kg}$ of liquid water at $0.0^{\circ} \mathrm{C}$.

Narayan Hari

Numerade Educator

Problem 54

A person eats a container of strawberry yogurt. The Nutritional Facts label states that it contains 240 Calories ( 1 Calorie $=4186 \mathrm{~J}$ ). What mass of perspiration would one have to lose to get rid of this energy? At body temperature, the latent heat of vaporization of water is $2.42 \times 10^{6} \mathrm{~J} / \mathrm{kg} .$

Vinnu M

Numerade Educator

Problem 55

Liquid nitrogen boils at a chilly $-195.8^{\circ} \mathrm{C}$ when the pressure is one atmosphere. A silver coin of mass $1.5 \times 10^{2} \mathrm{~kg}$ and temperature $25{ }^{\circ} \mathrm{C}$ is dropped into the boiling liquid. What mass of nitrogen boils off as the coin cools to $-195.8^{\circ} \mathrm{C} ?$

Narayan Hari

Numerade Educator

Problem 56

A $10.0-\mathrm{kg}$ block of ice has a temperature of $-10.0^{\circ} \mathrm{C}$. The pressure is one atmosphere. The block absorbs $4.11 \times 10^{6} \mathrm{~J}$ of heat. What is the final temperature of the liquid water?

Narayan Hari

Numerade Educator

Problem 57

A woman finds the front windshield of her car covered with ice at $-12.0^{\circ} \mathrm{C}$. The ice has a thickness of $4.50 \times 10^{-4} \mathrm{~m},$ and the windshield has an area of $1.25 \mathrm{~m}^{2}$. The density of ice is $917 \mathrm{~kg} / \mathrm{m}^{3}$. How much heat is required to melt the ice?

Narayan Hari

Numerade Educator

Problem 58

A thermos contains $150 \mathrm{~cm}^{3}$ of coffee at $85^{\circ} \mathrm{C}$. To cool the coffee, you drop two $11-\mathrm{g}$ ice cubes into the thermos. The ice cubes are initially at $0^{\circ} \mathrm{C}$ and melt completely. What is the final temperature of the coffee? Treat the coffee as if it were water.

Sanjeev Kumar

Numerade Educator

Problem 59

Ice at $-10.0^{\circ} \mathrm{C}$ and steam at $130{ }^{\circ} \mathrm{C}$ are brought together at atmospheric pressure in a perfectly insulated container. After thermal equilibrium is reached, the liquid phase at $50.0^{\circ} \mathrm{C}$ is present. Ignoring the container and the equilibrium vapor pressure of the liquid at $50.0^{\circ} \mathrm{C},$ find the ratio of the mass of steam to the mass of ice. The specific heat capacity of steam is $2020 \mathrm{~J} /\left(\mathrm{kg} \cdot \mathrm{C}^{\circ}\right)$.

Manish Jain

Numerade Educator

Problem 60

Equal masses of two different liquids have the same temperature of $25.0^{\circ} \mathrm{C}$. Liquid A has a freezing point of $-68.0{ }^{\circ} \mathrm{C}$ and a specific heat capacity of $1850 \mathrm{~J} /\left(\mathrm{kg} \cdot \mathrm{C}^{\circ}\right) .$ Liquid $\mathrm{B}$ has a freezing point of $-96.0^{\circ} \mathrm{C}$ and a specific heat capacity of $2670 \mathrm{~J} /\left(\mathrm{kg} \cdot \mathrm{C}^{\circ}\right) .$ The same amount of heat must be removed from each liquid in order to freeze it into a solid at its respective freezing point. Determine the difference $L_{\mathrm{f}, \mathrm{A}}-L_{\mathrm{f}, \mathrm{B}}$ between the latent heats
of fusion for these liquids.

Mayukh Banik

Numerade Educator

Problem 61

Interactive Solution $\underline{12.61} 12.61$ at provides a model for solving problems such as this. A $42-\mathrm{kg}$ block of ice at $0{ }^{\circ} \mathrm{C}$ is sliding on a horizontal surface. The initial speed of the ice is $7.3 \mathrm{~m} / \mathrm{s}$ and the final speed is $3.5 \mathrm{~m} / \mathrm{s}$. Assume that the part of the block that melts has a very small mass and that all the heat generated by kinetic friction goes into the block of ice, and determine the mass of ice that melts into water at $0^{\circ} \mathrm{C}$.

Narayan Hari

Numerade Educator

Problem 62

Water at $23.0^{\circ} \mathrm{C}$ is sprayed onto $0.180 \mathrm{~kg}$ of molten gold at $1063^{\circ} \mathrm{C}$ (its melting point). The water boils away, forming steam at $100.0^{\circ} \mathrm{C}$ and leaving solid gold at $1063^{\circ} \mathrm{C}$. What is the minimum mass of water that must be used?

Mayukh Banik

Numerade Educator

Problem 63

An unknown material has a normal melting/ freezing point of $-25.0^{\circ} \mathrm{C},$ and the liquid phase has a specific heat capacity of $160 \mathrm{~J} /\left(\mathrm{kg} \cdot \mathrm{C}^{\circ}\right)$. One-tenth of a kilogram of the solid at $-25.0^{\circ} \mathrm{C}$ is put into a $0.150-\mathrm{kg}$ aluminum calorimeter cup that contains 0.100 kg of glycerin. The temperature of the cup and the glycerin is initially $27.0^{\circ} \mathrm{C}$. All the unknown material melts, and the final temperature at equilibrium is $20.0^{\circ} \mathrm{C}$. The calorimeter neither loses energy to nor gains energy from the external environment. What is the latent heat of fusion of the unknown material?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 64

To help keep his barn warm on cold days, a farmer stores $840 \mathrm{~kg}$ of solar-heated water $\left(L_{\mathrm{f}}=3.35 \times 10^{5} \mathrm{~J} / \mathrm{kg}\right)$ in barrels. For how many hours would a $2.0-\mathrm{kW}$ electric space heater have to operate to provide the same amount of heat as the water does when it cools from 10.0 to $0.0^{\circ} \mathrm{C}$ and completely freezes?

Narayan Hari

Numerade Educator

Problem 65

It is claimed that if a lead bullet goes fast enough, it can melt completely when it comes to a halt suddenly, and all its kinetic energy is converted into heat via friction. Find the minimum speed of a lead bullet (initial temperature $=30.0^{\circ} \mathrm{C}$ ) for such an event to happen.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 66

A locomotive wheel is $1.00 \mathrm{~m}$ in diameter. A $25.0-\mathrm{kg}$ steel band has a temperature of $20.0^{\circ} \mathrm{C}$ and a diameter that is $6.00 \times 10^{-4} \mathrm{~m}$ less than that of the wheel. What is the smallest mass of water vapor at $100^{\circ} \mathrm{C}$ that can be condensed on the steel band to heat it, so that it will fit onto the wheel? Do not ignore the water that results from the condensation.

Ummatul Choudary

Ummatul Choudary

Numerade Educator

Problem 67

ssm Use the vapor pressure curve that accompanies this problem to determine the temperature at which liquid carbon dioxide exists in equilibrium with its vapor phase when the vapor pressure is $3.6 \times 10^{6} \mathrm{~Pa}$.

Satpal Satpal

Numerade Educator

Problem 68

At a temperature of $10^{\circ} \mathrm{C}$ the percent relative humidity is $R_{10}$, and at $40{ }^{\circ} \mathrm{C}$ it is $R_{40}$. At
each of these temperatures the partial pressure of water vapor in the air is the same. Using the vapor pressure curve for water that accompanies this problem, determine the ratio $R_{10} / R_{40}$ of the two humidity values.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 69

The relative humidity is $35 \%$ when the temperature is $27^{\circ} \mathrm{C}$. Using the vapor pressure curve for water that accompanies problem 68 . determine the dew point.

Narayan Hari

Numerade Educator

Problem 70

Suppose that air in the human lungs has a temperature of $37^{\circ} \mathrm{C},$ and the partial pressure of water vapor has a value of $5.5 \times 10^{3} \mathrm{~Pa}$. What is the relative humidity in the lungs? Consult the vapor pressure curve for water that accompanies problem 68 .

Narayan Hari

Numerade Educator

Problem 71

The temperature of $2.0 \mathrm{~kg}$ of water is $100.0{ }^{\circ} \mathrm{C},$ but the water is not boiling, because the external pressure acting on the water surface is $3.0 \times 10^{5} \mathrm{~Pa}$. Using the vapor pressure curve for water given in Figure $12-33,$ determine the amount of heat that must be added to the water to bring it to the point where it just begins to boil.

Mayukh Banik

Numerade Educator

Problem 72

The temperature of the air in a room is $36^{\circ} \mathrm{C}$. A person turns on a dehumidifier and notices that when the cooling coils reach $30^{\circ} \mathrm{C}$, water begins to condense on them. What is the relative humidity in the room? Use the vapor pressure curve that accompanies problem 68.

Narayan Hari

Numerade Educator

Problem 73

A woman has been outdoors where the temperature is $10^{\circ} \mathrm{C}$. She walks into a $25^{\circ} \mathrm{C}$ house, and her glasses "steam up." Using the vapor pressure curve for water that accompanies problem $68,$ find the smallest possible value for the relative humidity of the
room.

Narayan Hari

Numerade Educator

Problem 74

A container is fitted with a movable piston of negligible mass and radius $r=0.061 \mathrm{~m}$. Inside the container is liquid water in equilibrium with its vapor, as the drawing shows. The piston remains stationary with a $120-\mathrm{kg}$ block on top of it. The air pressure acting on the top of the piston is one atmosphere. By using the vaporization curve for water in Figure $12-33,$ find the temperature of the water.

Mayukh Banik

Numerade Educator

Problem 75

ssm At a picnic, a glass contains $0.300 \mathrm{~kg}$ of tea at $30.0{ }^{\circ} \mathrm{C}$, which is the air temperature. To make iced tea, someone adds $0.0670 \mathrm{~kg}$ of ice at $0.0^{\circ} \mathrm{C}$ and stirs the mixture. When all the ice melts and the final temperature is reached, the glass begins to fog up, because water vapor condenses on the outer glass surface. Using the vapor pressure curve for water that accompanies problem 68 , ignoring the specific heat capacity of the glass, and treating the tea as if it were water, estimate the relative humidity.

Ummatul Choudary

Ummatul Choudary

Numerade Educator

Problem 76

A tall column of water is open to the atmosphere. At a depth of $10.3 \mathrm{~m}$ below the surface, the water is boiling. What is the temperature at this depth? Use the vaporization curve for water in Figure $12-33,$ as needed.

Mayukh Banik

Numerade Educator

Problem 77

A steel aircraft carrier is $370 \mathrm{~m}$ long when moving through the icy North Atlantic at a temperature of $2.0^{\circ} \mathrm{C} .$ By how much does the carrier lengthen when it is traveling in the warm Mediterranean Sea at a temperature of $21^{\circ} \mathrm{C} ?$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 78

The latent heat of vaporization of $\mathrm{H}_{2} \mathrm{O}$ at body temperature $\left(37.0^{\circ} \mathrm{C}\right)$ is $2.42 \times 10^{6} \mathrm{~J} / \mathrm{kg} .$ To cool the body of a $75-\mathrm{kg}$ jogger [average specific heat capacity $\left.=3500 \mathrm{~J} /\left(\mathrm{kg} \cdot \mathrm{C}^{\circ}\right)\right]$ by $1.5 \mathrm{C}^{\circ},$ how many kilograms of water in the form of sweat have to be evaporated?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 79

Find the mass of water that vaporizes when $2.10 \mathrm{~kg}$ of mercury at $205{ }^{\circ} \mathrm{C}$ is added to $0.110 \mathrm{~kg}$ of water at $80.0^{\circ} \mathrm{C}$.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 80

A $0.200-\mathrm{kg}$ piece of aluminum that has a temperature of $-155^{\circ} \mathrm{C}$ is added to $1.5 \mathrm{~kg}$ of water that has a temperature of $3.0^{\circ} \mathrm{C}$. At equilibrium the temperature is $0.0^{\circ} \mathrm{C}$. Ignoring the container and assuming that the heat exchanged with the surroundings is negligible, determine the mass of water that has been frozen into ice.

Mayukh Banik

Numerade Educator

Problem 81

A commonly used method of fastening one part to another part is called "shrink fitting." A steel rod has a diameter of $2.0026 \mathrm{~cm}$, and a flat plate contains a hole whose diameter is $2.0000 \mathrm{~cm}$. The rod is cooled so that it just fits into the hole. When the rod warms up, the enormous thermal stress exerted by the plate holds the rod securely to the plate. By how many Celsius degrees should the rod be cooled?

Vinnu M

Numerade Educator

Problem 82

A thin rod consists of two parts joined together. One-third of it is silver and two-thirds is gold. The temperature decreases by $26 \mathrm{C}^{\circ} .$ Determine the fractional decrease $\frac{\Delta L}{L_{0, \text { Silver }}+L_{0, \text { Gold }}}$ in the rod's length, where $L_{0, \text { Silver }}$ and $L_{0, \text { Gold }}$ are the initial lengths of the silver and gold rods.

Mayukh Banik

Numerade Educator

Problem 83

Suppose you are selling apple cider for two dollars a gallon when the temperature is $4.0^{\circ} \mathrm{C} .$ The coefficient of volume expansion of the cider is $280 \times 10^{6}\left(\mathrm{C}^{\circ}\right)^{-1} .$ If the expansion of the container is ignored, how much more money (in pennies) would you make per gallon by refilling the container on a day when the temperature is $26^{\circ} \mathrm{C} ?$

Satpal Satpal

Numerade Educator

Problem 84

Ideally, when a thermometer is used to measure the temperature of an object, the temperature of the object itself should not change. However, if a significant amount of heat flows from the object to the thermometer, the temperature will change. A thermometer has a mass of $31.0 \mathrm{~g},$ a specific heat capacity of $c=815 \mathrm{~J} /\left(\mathrm{kg} \cdot \mathrm{C}^{\circ}\right),$ and a temperature of $12.0^{\circ} \mathrm{C}$. It is immersed in $119 \mathrm{~g}$ of water, and the final temperature of the water and thermometer is $41.5^{\circ} \mathrm{C}$. What was the temperature of the water before the insertion of the thermometer?

Narayan Hari

Numerade Educator

Problem 85

What is the relative humidity on a day when the temperature is $30^{\circ} \mathrm{C}$ and the dew point is $10^{\circ} \mathrm{C}$ ? Use the vapor pressure curve that accompanies problem 68 .

Narayan Hari

Numerade Educator

Problem 86

A copper-constantan thermocouple can generate a voltage of $4.75 \times 10^{-3}$ volts when the temperature of the hot junction is $110.0{ }^{\circ} \mathrm{C}$ and the reference junction is kept at $0.0^{\circ}$
C. If the voltage is proportional to the difference in temperature between the junctions, what is the temperature of the hot junction when the voltage is $1.90 \times 10^{-3}$ volts?

Narayan Hari

Numerade Educator

Problem 87

Occasionally, huge icebergs are found floating on the ocean's currents. Suppose one such iceberg is $120 \mathrm{~km}$ long, $35 \mathrm{~km}$ wide, and $230 \mathrm{~m}$ thick. (a) How much heat would be required to melt this iceberg (assumed to be at $0^{\circ} \mathrm{C}$ ) into liquid water at $0^{\circ} \mathrm{C}$ ? The density of ice is $917 \mathrm{~kg} / \mathrm{m}^{3}$. (b) The annual energy consumption by the United States in 1994 was $9.3 \times 10^{19} \mathrm{~J}$. If this energy were delivered to the iceberg every year, how many years would it take before the ice melted?

Narayan Hari

Numerade Educator

Problem 88

Two grams of liquid water are at $0^{\circ} \mathrm{C},$ and another two grams are at $100^{\circ} \mathrm{C}$. Heat is removed from the water at $0^{\circ} \mathrm{C}$, completely freezing it at $0^{\circ} \mathrm{C}$. This heat is then used to vaporize some of the water at $100{ }^{\circ} \mathrm{C}$. What is the mass (in grams) of the liquid water that remains?

Narayan Hari

Numerade Educator

Problem 89

Refer to Interactive LearningWare 12.2 at for a review of the concepts that play roles in this problem. The box of a well-known breakfast cereal states that one ounce of the cereal contains 110 Calories ( 1 food Calorie $=4186 \mathrm{~J}$ ). If $2.0 \%$ of this energy could be converted by a weight lifter's body into work done in lifting a barbell, what is the heaviest barbell that could be lifted a distance of $2.1 \mathrm{~m} ?$

Narayan Hari

Numerade Educator

Problem 90

Multiple-Concept Example 4 illustrates the concepts pertinent to this problem. A cylindrical brass rod (cross - sectional area $=1.3 \times 10^{-5} \mathrm{~m}^{2}$ ) hangs vertically straight down from a ceiling. When an $860-\mathrm{N}$ block is hung from the lower end of the rod, the rod stretches. The rod is then cooled such that it contracts to its original length. By how many degrees must the temperature be lowered?

Vinnu M

Numerade Educator

Problem 91

A rock of mass 0.20 kg falls from rest from a height of $15 \mathrm{~m}$ into a pail containing $0.35 \mathrm{~kg}$ of water. The rock and water have the same initial temperature. The specific heat capacity of the rock is $1840 \mathrm{~J} /\left(\mathrm{kg} \cdot \mathrm{C}^{\circ}\right)$. Ignore the heat absorbed by the pail itself, and determine the rise in the temperature of the rock and water.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 92

A steel ruler is calibrated to read true at $20.0^{\circ} \mathrm{C}$. A draftsman uses the ruler at $40.0^{\circ} \mathrm{C}$ to draw a line on a $40.0^{\circ} \mathrm{C}$ copper plate. As indicated on the warm ruler, the length of the line is $0.50 \mathrm{~m}$. To what temperature should the plate be cooled, such that the length of the line truly becomes $0.50 \mathrm{~m} ?$

Narayan Hari

Numerade Educator

Problem 93

A steel rod $\left(\rho=7860 \mathrm{~kg} / \mathrm{m}^{3}\right)$ has a length of $2.0 \mathrm{~m}$. It is bolted at both ends between immobile supports. Initially there is no tension in the rod, because the rod just fits between the supports. Find the tension that develops when the rod loses $3300 \mathrm{~J}$ of heat.

Vinnu M

Numerade Educator

Problem 94

An $85.0-\mathrm{N}$ backpack is hung from the middle of an aluminum wire, as the drawing shows. The temperature of the wire then drops by $20.0 \mathrm{C}^{\circ} .$ Find the tension in the wire at the lower temperature. Assume that the distance between the supports does not change, and ignore any thermal stress.

Mayukh Banik

Numerade Educator

Problem 95

Concept Questions The drawing shows two thermometers, $A$ and $B$, whose temperatures are measured in ${ }^{\circ} \mathrm{A}$ and ${ }^{\circ} \mathrm{B}$. The ice and boiling points of water are also indicated. (a) Is the size of one degree on the A scale larger than, the same as, or smaller than on the B scale? Why? (b) Is a given temperature on the A scale (e.g., $+20^{\circ} \mathrm{A}$ ) hotter than, the same as, or colder than the same reading on the B scale (e.g., $+20^{\circ} \mathrm{B}$ )? Provide a reason for your answer.

Problem (a) Using the data in the drawing, determine the number of $\mathrm{B}^{\circ}$ on the B scale that correspond to $1 \mathrm{~A}^{\circ}$ on the A scale. (b) If the temperature of a substance reads $+40.0^{\circ}$ A on the A scale, what would that temperature read on the B scale?

Ummatul Choudary

Ummatul Choudary

Numerade Educator

Problem 96

Concept Questions (a) When an object, such as a rod, is heated, what factors determine how much its length increases? (b) Suppose two rods are made from materials that have different coefficients of linear expansion, but their lengths change by the same amount when their temperatures change by the same amount. Are their initial lengths the same or different? Explain.
Problem One rod is made from lead and another from quartz. They are heated and experience the same change in temperature. If the initial length of the lead rod is $0.10 \mathrm{~m}$, what is the initial length of the quartz rod? Be sure that your answer is consistent with your answer to the Concept Questions.

Manish Jain

Numerade Educator

Problem 97

Concept Questions An aluminum can is filled to the brim with a liquid. The can and the liquid are heated so their temperatures change by the same amount. (a) In general, what factors determine how the volume of an object changes when it is heated?
(b) Aluminum has a smaller coefficient of volume expansion than the liquid does. Which, if either, will expand more, the can or the liquid? Provide a reason for your answer. (c) How is the volume of liquid that spills over related to the changes in the volume of the can and the liquid?

Ummatul Choudary

Ummatul Choudary

Numerade Educator

Problem 98

Concept Questions (a) When heat is added to an object, what factors determine its change in temperature, assuming there is no phase change? (b) Suppose the same amount of heat is applied to two bars without their changing phase. They have the same mass, but experience different changes in temperature. Are the specific heat capacities the same for each bar? Why or why not?
Problem Two bars of identical mass are at $25^{\circ} \mathrm{C}$. One is made from glass and the other from another substance. When identical amounts of heat are supplied to each, the glass bar reaches a temperature of $88^{\circ} \mathrm{C}$, while the other reaches $250.0{ }^{\circ} \mathrm{C}$. What is the specific heat capacity of the other substance?

Manish Jain

Numerade Educator

Problem 99

Concept Questions Suppose you have two solid objects, $\mathrm{A}$ and $\mathrm{B},$ made from different materials. They have the same mass, and each solid is at its melting temperature. You then add heat to melt them. (a) It takes less heat to melt A than B. Which, if either, has the larger latent heat of fusion? Explain. (b) The mass of each is doubled. Does it require twice as much heat to melt them? Justify your answer.
Problem (a) Objects $A$ and $B$ have the same mass of $3.0 \mathrm{~kg} .$ They melt when $3.0 \times 10^{4} \mathrm{~J}$ of heat is added to $\mathrm{A}$ and $9.0 \times 10^{4} \mathrm{~J}$ is added to $\mathrm{B}$. Determine the latent heats of fusion. (b) Find the heat required to melt object A when its mass is $6.0 \mathrm{~kg}$. Verify that your answers are consistent with your answers to the Concept Questions.

Manish Jain

Numerade Educator

Problem 100

Concept Questions On a cool autumn morning, the relative humidity is $100 \%$. (a) Does this mean that the partial pressure of water in the air equals atmospheric pressure? Why or why not? (b) Suppose the air warms up in the afternoon, but the partial pressure of water in the air does not change. Is the humidity still $100 \% ?$ Provide a reason for your answer. Problem The vapor pressure of water at $20^{\circ} \mathrm{C}$ is $2500 \mathrm{~Pa}$. (a) What percentage of atmospheric pressure is this? (b) What percentage of the total air pressure at $20^{\circ} \mathrm{C}$ is due to water vapor if the relative humidity is $100 \% ?$ (c) The vapor pressure of water at $35^{\circ} \mathrm{C}$ is $5500 \mathrm{~Pa}$. What is the relative humidity at this temperature if the partial pressure of water in the air has not changed from that at $20^{\circ} \mathrm{C} ?$

Manish Jain

Numerade Educator

Problem 101

Concept Questions (a) A ball and a thin plate are made from different materials and have the same initial temperature. The ball does not fit through a hole in the plate, because the diameter of the ball is slightly larger than the diameter of the hole. However, the ball will pass through the hole when the ball and the plate are both heated to a common higher temperature. How do the coefficients of linear expansion of the ball and the plate compare? Explain. (b) The drawing shows three ball/plate arrangements like that in Concept Question (a). In each, the diameters of the balls are the same, and the diameters of the holes are the same. As the temperature increases, which ball falls through the hole first, which second, and which third? Account for your answers with the aid of data from Table $12-1$. Problem In each of the arrangements in the drawing the diameter of the ball is $1.0 \times 10^{-5} \mathrm{~m}$ larger than the diameter of the hole, which has a diameter of $0.10 \mathrm{~m}$. The initial temperature of each arrangement is $25.0^{\circ} \mathrm{C}$. At what temperature will the ball fall through the hole in each arrangement? Verify that your answer is consistent with your answer to Concept Question (b).

Manish Jain

Numerade Educator

Problem 102

Concept Questions (a) Two portions of the same liquid have the same mass, but different temperatures. They are mixed in a container that prevents the exchange of heat with the environment. Portion A has the higher initial temperature of $T_{0 \mathrm{~A}},$ while
portion $\mathrm{B}$ has an initial temperature of $T_{0 \mathrm{~B}}$. Relative to these two temperatures, where
on the temperature scale will the final equilibrium temperature of the mixture be located? Explain. (b) Three portions of the same liquid are mixed in a container that prevents the exchange of heat with the environment. Portion A has a mass $m$ and a temperature of $94.0^{\circ} \mathrm{C}$, portion $\mathrm{B}$ has a mass $m$ and a temperature of $78.0^{\circ} \mathrm{C},$ and portion $\mathrm{C}$ has a mass $2 \mathrm{~m}$ and a temperature of $34.0{ }^{\circ} \mathrm{C}$. Considering your answer to Concept Question (a) and without doing a heat-lost-equals-heat-gained calculation, deduce the final temperature of the mixture at equilibrium. Justify your answer. Problem Three portions of the same liquid are mixed in a container that prevents the exchange of heat with the environment. Portion A has a mass $m$ and a temperature of $94.0^{\circ} \mathrm{C},$ portion $\mathrm{B}$ has a mass $m$ and a temperature of $78.0{ }^{\circ} \mathrm{C},$ and portion $\mathrm{C}$ has a mass $m_{\mathrm{C}}$ and a temperature of $34.0^{\circ} \mathrm{C}$. What must be the mass of portion $\mathrm{C}$ such that the final temperature $T_{\mathrm{f}}$ of the three-portion mixture is $T_{\mathrm{f}}=50.0^{\circ} \mathrm{C} ?$ Express your answer in terms of $m ;$ e.g., $m_{C}=2.20 m$.

Manish Jain

Numerade Educator