Temperature and heat | Practice Problems, Examples & Solutions

Temperature and Thermal Equilibrium

Chemistry: Introducing Inorganic, Organic and Physical Chemistry

A student used a calorimeter containing $100 \mathrm{g}$ of deionized water which required an energy change of $818 \mathrm{J}$ to cause a temperature change of $1 \mathrm{K}$
An unknown mass of sodium hydroxide, NaOH, was dissolved in the water and the temperature rose from $25.00^{\circ} \mathrm{C}$ to $31.00^{\circ} \mathrm{C}$. Given that the molar enthalpy of solution of NaOH is $-44.51 \mathrm{kJ} \mathrm{mol}^{-1}$, what mass of sodium hydroxide was dissolved? (Section 13.6)

Energy and thermochemistry

02:44

Chemistry: Introducing Inorganic, Organic and Physical Chemistry

"The density of nitrogen gas in a container at $300 \mathrm{K}$ and 1.0 bar pressure is $1.25 \mathrm{g} \mathrm{dm}^{-3}$ (Section 8.5 ).
(a) Calculate the rms speed of the molecules.
(b) At what the temperature will the ms speed be twice as fast?

Gases

01:57

Chemistry: Introducing Inorganic, Organic and Physical Chemistry

Predict which compound in each of the following pairs has the higher decomposition temperature: (a) $\mathrm{NaNO}_{3}$ and $\mathrm{KNO}_{3}$ (b) $\mathrm{LiH}$ and $\mathrm{KH} ;(\mathrm{c}) \mathrm{Li}_{2} \mathrm{CO}_{3}$ and $\mathrm{SrCO}_{3}$. Give reasons for your answer. (Section 26.2).

s-Block chemistry

Thermometers and Temperature Scales

134 Practice Problems

00:58

Physics Principle and Problems

Conversions Convert the following Celsius temperatures to Kelvin temperatures.
a. $28^{\circ} \mathrm{C}$
b. $154^{\circ} \mathrm{C}$
c. $568^{\circ} \mathrm{C}$
d. $-55^{\circ} \mathrm{C}$
e. $-184^{\circ} \mathrm{C}$

Thermal Energy

Temperature and Thermal Energy

01:41

Physics Principle and Problems

Find the Celsius and Kelvin temperatures for the following.
a. room temperature
c. a hot summer day in North Carolina
b. a typical refrigerator
d. a winter night in Minnesota

Thermal Energy

Temperature and Thermal Energy

02:00

Physics Principle and Problems

Convert the following Kelvin temperatures to Celsius temperatures.
a. $115 \mathrm{K}$
c. $125 \mathrm{K}$
e. $425 \mathrm{K}$
b. $172 \mathrm{K}$
d. $402 \mathrm{K}$
f. $212 \mathrm{K}$

Thermal Energy

Temperature and Thermal Energy

Gas Thermometers and the Kelvin Scale

60 Practice Problems

01:13

Fundamentals of Thermodynamics

Prove that a cyclic device that violates the Kelvin-Planck statement of the second law also violates the Clausius statement of the second law.

The Second Law of Thermodynamics

00:32

Thermodynamics : An Engineering Approach

It is well known that warm air in a cooler environment rises. Now consider a warm mixture of air and gasoline on top of an open gasoline can. Do you think this gas mixture will rise in a cooler environment?

Properties of Pure Substances

00:51

Thermodynamics : An Engineering Approach

In what kind of pot will a given volume of water boil at a higher temperature: a tall and narrow one or a short and wide one? Explain.

Properties of Pure Substances

Thermal Expansion

76 Practice Problems

01:09

Physical Chemistry: A Molecular Approach

The coefficient of thermal expansion $\alpha$ is defined as
\[\alpha=\frac{1}{\bar{V}}\left(\frac{\partial \bar{V}}{\partial T}\right)_{p}\]
Show that
\[\alpha=\frac{1}{T}\]
for an ideal gas.

The Properties of Gases

05:40

Fundamentals of Thermodynamics

Helium gas expands from $125 \mathrm{kPa}, 350 \mathrm{K}$ and $0.25 \mathrm{m}^{3}$ to $100 \mathrm{kPa}$ in a polytropic process with $n=1.667 .$ How much heat transfer is involved?

The First Law of Thermodynamics

02:27

Fundamentals of Thermodynamics

An ideal gas goes through an expansion process whereby the volume doubles. Which process will lead to the larger work output, an isothermal process or a polytropic process with $n=1.25 ?$

Work and Heat

Quantity of Heat

247 Practice Problems

02:29

Physical Chemistry

What is the heat evolved in freezing water at $-10^{\circ} \mathrm{Cgiven}$ that
$$\begin{aligned}
\mathrm{H}_{2} \mathrm{O}(\mathrm{l}) &=\mathrm{H}_{2} \mathrm{O}(\mathrm{s}) \quad \Delta H^{\circ}(273 \mathrm{K})=-6004 \mathrm{J} \mathrm{mol}^{-1} \\
\bar{C}_{P}\left(\mathrm{H}_{2} \mathrm{O}, \mathrm{l}\right) &=75.3 \mathrm{J} \mathrm{K}^{-1} \mathrm{mol}^{-1} \\
\bar{C}_{P}\left(\mathrm{H}_{2} \mathrm{O}, \mathrm{s}\right) &=36.8 \mathrm{J} \mathrm{K}^{-1} \mathrm{mol}^{-1}
\end{aligned}$$

First Law of Thermodynamics

03:07

Physical Chemistry

Liquid water is vaporized at $100^{\circ} \mathrm{C}$ and 1.013 bar. The heat of vaporization is $40.69 \mathrm{kJ} \mathrm{mol}^{-1} .$ What are the values of
$(a) w_{\mathrm{rev}}$ per mole, $(b) q$ per mole,
$(c) \Delta \bar{U},$ and
$(d) \Delta \bar{H} ?$

First Law of Thermodynamics

03:48

Introduction to General, Organic and Biochemistry

Heats of reaction are frequently measured by monitoring the change in temperature of a water bath in which the reaction mixture is immersed. A water bath used for this purpose contains 2.000 L of water. In the course of the reaction, the temperature of the water rose $4.85^{\circ} \mathrm{C}$
(a) How many calories were liberated by the reaction?
(b) If $2 \mathrm{kg}$ of a given reactant is consumed in the reaction, how many calories are liberated for each kilogram?

Chemical Reactions and Energy Calculations

Calorimetry and Phase Changes

21 Practice Problems

03:10

Principles of Physics a Calculus Based Text

If water with a mass $m_{h}$ at temperature $T_{h}$ is poured into an aluminum cup of mass $m_{\mathrm{M}}$ containing mass $m_{c}$ of water at $T_{c},$ where $T_{h}>T_{c},$ what is the equilibrium temperature of the system?

Energy in Thermal Processes: The First Law of Thermodynamics

07:13

Principles of Physics a Calculus Based Text

An aluminum calorimeter with a mass of $100 \mathrm{g}$ contains $250 \mathrm{g}$ of water. The calorimeter and water are in thermal equilibrium at $10.0^{\circ} \mathrm{C}$. Two metallic blocks are placed into the water. One is a 50.0 -g piece of copper at $80.0^{\circ} \mathrm{C}$. The other has a mass of $70.0 \mathrm{g}$ and is originally at a temperature of $100^{\circ} \mathrm{C}$. The entire system stabilizes at a final temperature of $20.0^{\circ} \mathrm{C}$. (a) Determine the specific heat of the unknown sample. (b) Using the data in Table 17.1 , can you make a positive identification of the unknown material? Can you identify a possible material? (c) Explain your answers for part (b).

Energy in Thermal Processes: The First Law of Thermodynamics

06:44

Chemistry

A hemoglobin molecule (molar mass $=65,000 \mathrm{g}$ ) can bind up to four oxygen molecules. In a certain experiment a $0.085-\mathrm{L}$ solution containing $6.0 \mathrm{g}$ of deoxyhemoglobin (hemoglobin without oxygen molecules bound to it) was reacted with an excess of oxygen in a constant-pressure calorimeter of negligible heat capacity. Calculate the enthalpy of reaction per mole of oxygen bound if the temperature rose by $0.044^{\circ} \mathrm{C}$. Assume the solution is dilute so that the specific heat of the solution is equal to that of water.

Thermochemistry

Mechanisms of Heat Transfer

102 Practice Problems

01:59

Atkins' Physical Chemistry

Silylene $\left(\mathrm{SiH}_{2}\right)$ is a key intermediate in the thermal decomposition of silicon hydrides such as silane $\left(\mathrm{SiH}_{4}\right)$ and disilane $\left(\mathrm{Si}_{2} \mathrm{H}_{6}\right) .$ H.K. Moffat et al.
U. Phys. Chem. $95,145(1991)$ ) report $\Delta_{i} H^{\ominus}\left(\mathrm{SiH}_{2}\right)=+274 \mathrm{kJ} \mathrm{mol}^{-1}$. Given that
$\Delta_{1} H^{\ominus}\left(\mathrm{SiH}_{4}\right)=+34.3 \mathrm{kJ} \mathrm{mol}^{-1}$ and $\Delta_{i} H^{\ominus}\left(\mathrm{Si}_{2} \mathrm{H}_{6}\right)=+80.3 \mathrm{kJ} \mathrm{mol}^{-1},$ calculate
the standard enthalpy changes of the following reactions:
(a) $\quad \operatorname{SiH}_{4}(g) \rightarrow \operatorname{SiH}_{2}(g)+H_{2}(g)$
(b) $\quad \operatorname{Si}_{2} \mathrm{H}_{6}(\mathrm{g}) \rightarrow \operatorname{SiH}_{2}(\mathrm{g})+\operatorname{SiH}_{4}(\mathrm{g})$

The First Law

Thermochemistry

01:21

Atkins' Physical Chemistry

The standard enthalpy of combustion of cyclopropane is $-2091 \mathrm{kJ} \mathrm{mol}^{-1}$ at $25^{\circ} \mathrm{C}$. (a) From this information and enthalpy of formation data for $\mathrm{CO}_{2}(\mathrm{g})$ and $\mathrm{H}_{2} \mathrm{O}(\mathrm{l}),$ calculate the enthalpy of formation of cyclopropane.
(b) The enthalpy of formation of propene is $+20.42 \mathrm{kJ} \mathrm{mol}^{-1}$. Calculate the enthalpy of isomerization of cyclopropane to propene.

The First Law

Thermochemistry

18:49

Atkins' Physical Chemistry

An average human produces about $10 \mathrm{MJ}$ of heat each day through metabolic activity. If a human body were an isolated system of mass $65 \mathrm{kg}$ with the heat capacity of water, what temperature rise would the body experience? Human bodies are actually open systems, and the main mechanism of heat loss is through the evaporation of water. What mass of water should be evaporated each day to maintain constant temperature?

The First Law

Thermochemistry

Zeroth Law of Thermodynamics

4 Practice Problems

02:52

University Physics

Give an example in which $A$ has some kind of nonthermal equilibrium relationship with $B$, and $B$ has the same relationship with $C,$ but $A$ does not have that relationship with $C$.

Temperature and Heat

01:17

Physics: A Conceptual World View

Imagine a universe where the zeroth law of thermodynamics was not valid. Would the concept of temperature still make sense in this universe? Why or why not?

Thermal Energy

00:56

Physics: A Conceptual World View

It could be argued that the only time you measure the undisturbed temperature of a system is when the reading on the thermometer does not change when it is placed in thermal contact with the system. Use the zeroth law to explain why this is so.

Thermal Energy

Ideal Gas

136 Practice Problems

02:45

Physical Chemistry

An ideal monatomic gas at 1 bar and $300 \mathrm{K}$ is expanded adiabatically against a constant pressure of $\frac{1}{2}$ bar until the final pressure is $\frac{1}{2}$ bar. What are the values of $q$ per mole, $w$ per mole, $\Delta \bar{U},$ and $\Delta \bar{H} ?$ Given: $\bar{C}_{V}=\frac{3}{2} R$.

First Law of Thermodynamics

04:47

Physical Chemistry

The intensive state of an ideal gas can be completely defined by specifying $(1) T, P,(2) T, \bar{V},$ or $(3) P, \bar{V} .$ The extensive state of an ideal gas can be specified in four ways. What are the combinations of properties that can be used to specify the extensive state of an ideal gas? Although these choices are deduced for an ideal gas, they also apply to real gases.

Zeroth Law of Thermodynamics and Equations of State

01:28

Physical Chemistry: A Molecular Approach

Recall from general chemistry that Dalton's law of partial pressures says that each gas in a mixture of ideal gases acts as if the other gases were not present. Use this fact to show that the partial pressure exerted by each gas is given by
\[P_{j}=\left(\frac{n_{j}}{\sum n_{j}}\right) P_{\text {total }}=y_{j} P_{\text {total }}\]
where $P_{j}$ is the partial pressure of the $j$ th gas and $y_{j}$ is its mole fraction.

The Properties of Gases

The Kinetic Theory of Gases

36 Practice Problems

03:06

Chemistry

At a certain temperature the speeds of six gaseous molecules in a container are $2.0,2.2,2.6,2.7,3.3,$ and $3.5 \mathrm{m} / \mathrm{s}$. Calculate the root-mean-square speed and the average speed of the molecules. These two average values are close to each other, but the root-mean-square value is always the larger of the two. Why?

Gases

00:51

University Physics

If one kind of molecule has double the radius of another and eight times the mass, how do their mean free paths under the same conditions compare? How do their mean free times compare?

The Kinetic Theory of Gases

00:43

Introductory Chemistry: An Active Learning Approach

What properties of gases are the result of the kinetic character of a gas? Explain.

Introduction to Gases