Arihant AIEEE Physics

D.B. Singh

Chapter 15

Heat, Temperature and Calorimetry - all with Video Answers

Educators

Chapter Questions

Problem 1

The temperature at which Centigrade thermometer and Kelvin thermometer gives the same reading, is:
(a) $4^{\circ}$
(b) $273^{\circ}$
(c) not possible
(d) $0^{\circ}$

Ajay Singhal

Ajay Singhal

Numerade Educator

Problem 2

What is the change in the temperature on Fahrenheit scale and on Kelvin scale, if a iron piece is heated from $30^{\circ}$ to $90^{\circ} \mathrm{C} ?$
(a) $108^{\circ} \mathrm{F}, 60 \mathrm{~K}$
(b) $100^{\circ} \mathrm{F}, 55 \mathrm{~K}$
(c) $100^{\circ} \mathrm{F}, 65 \mathrm{~K}$
(d) $60^{\circ} \mathrm{F}, 108 \mathrm{~K}$

Ajay Singhal

Numerade Educator

Problem 3

What is the resistance of the wire at $30^{\circ} \mathrm{C}$, if at $5^{\circ} \mathrm{C}$, the resistance of same wire is $200 \Omega$ and at $10^{\circ} \mathrm{C}$, the resistance is $200.2 \Omega ?$
(a) $200 \Omega$
(b) $201 \Omega$
(c) $204 \Omega$
(d) $195 \Omega$

Ajay Singhal

Numerade Educator

Problem 4

Which of the following carries anomalous expansion ?
(a) Mercury
(b) Water
(c) Copper
(d) Sodium

Ajay Singhal

Numerade Educator

Problem 5

Two thermometers are constructed in such a way that one has a spherical bulb and the other has elongated cylindrical bulb. The bulbs are made of same material and thickness. Then:
(a) spherical bulb will respond more quickly to temperature changes
(b) cylindrical bulb will respond more quickly to temperature changes.
(c) both bulbs will respond same to temperature changes
(d) none of both bulbs respond to temperature changes

Ajay Singhal

Numerade Educator

Problem 6

Mark correct option or options:
(a) Sun temperature is measured by radiation pyrometer
(b) Insect temperature is measured by thermocouple thermometer
(c) Moon's temperature is measured by berthometer
(d) All of the above

Ajay Singhal

Numerade Educator

Problem 7

The temperature of a point in space is given by $T=\left(x^{2}+y^{2}-z^{2}\right) .$ A mosquito located at $(1,1,2)$ desires to fly in such a direction that it will get heat as soon as possible. Then unit vector is :
(b) $-\frac{2}{3} \hat{1}-\frac{2}{3} \hat{j}+\frac{1}{3}$
(i) $\frac{2}{3} \hat{i}-\frac{2}{3} \hat{j}-\frac{1}{3}$
(d) none of these

Dheeraj Sharma

Numerade Educator

Problem 8

A bird is flying at a speed of $5 \mathrm{~m} / \mathrm{s}$ in the direction of the vector $4 \hat{i}+4 \hat{j}-2 \hat{k}$. The temperature of the region is given by $T=x^{2}+y^{2}-z^{2}$
The rate of increase of temperature per unit time, at the instant it passes through the point $(1,1,2)$ is :
(a) $\frac{60}{3}{ }^{\circ} \mathrm{C} / \mathrm{s}$
(b) $3^{\circ} \mathrm{C} / \mathrm{s}$
(c) $18^{\circ} \mathrm{C} / \mathrm{s}$
(d) $4^{\circ} \mathrm{C} / \mathrm{s}$

Dheeraj Sharma

Numerade Educator

Problem 9

At $30^{\circ} \mathrm{C}$, the hole in a steel plate has diameter of $0.99970$ $\mathrm{cm}$. A cylinder of diameter exactly $1 \mathrm{~cm}$ at $30^{\circ} \mathrm{C}$ is to be slide into the hole. To what temperature the plate must be heated ? (Given : $\alpha_{\text {steel }}=1.1 \times 10^{-5}{ }^{\circ} \mathrm{C}^{-1}$ )
(a) $58^{\circ} \mathrm{C}$
(b) $55^{\circ} \mathrm{C}$
(c) $57.3^{\circ} \mathrm{C}$
(d) $60^{\circ} \mathrm{C}$

Ajay Singhal

Numerade Educator

Problem 10

If same amount of heat is supplied to two identical spheres (one is hollow and other is solid), then:
(a) the expansion in hollow is greater than the solid
(b) the expansion in hollow is same as that in solid
(c) the expansion in hollow is lesser than the solid
(d) the temperature of both must be same to each other.

Ajay Singhal

Numerade Educator

Problem 11

The metal sheet shown in figure, with two holes cut of unequal diameters $a_{1}$ and $d_{2}\left(d_{1}>d_{2}\right)$. If the sheet is heated:
(a) both $d_{1}$ and $d_{2}$ will decrease
(b) both $d_{1}$ and $d_{2}$ will increase
(c) $d_{1}$ will increase, $d_{2}$ will decrease
(d) $d_{1}$ will decrease, $d_{2}$ will increase

Ajay Singhal

Numerade Educator

Problem 12

A steel scale gives correct reading at $t_{1}{ }^{\circ} \mathrm{C}$. When temperature changes to $t_{2}{ }^{\circ} \mathrm{C}$, then :
(a) if $t_{2}>t_{1}$, reading is greater than true value
(b) if $t_{2}>t_{1}$, reading is lesser than true value
(c) the reading is always equal to true value
(d) the reading is always less than true value

Ajay Singhal

Numerade Educator

Problem 13

At $20^{\circ} \mathrm{C}$, a steel ruler of $20 \mathrm{~cm}$ long is graduated to give correct reading, but when it is used at a temperature of $40^{\circ} \mathrm{C}$, what will be the actual length of the steel ruler? $\left[\alpha_{\text {stèel }}=1.2 \times 10^{-5}\left({ }^{\circ} \mathrm{C}\right)^{-1}\right]$
(a) $22.02 \mathrm{~cm}$
(b) $19.6 \mathrm{~cm}$
(c) $20.0048 \mathrm{~cm}$
(d) $18.0002 \mathrm{~cm}$

Ajay Singhal

Numerade Educator

Problem 14

The temperature of a pendulum, the time period of which is $t$, is raised by $\Delta T$. The change in its time period 15:
(a) $\frac{\overline{1}}{2} \alpha f \Delta T$
(b) $2 \alpha t \Delta T$
(c) $\frac{1}{2} \alpha \Delta T$
(d) $2 \alpha \Delta T$

Ajay Singhal

Numerade Educator

Problem 15

A second's pendulum clock having steel wire is calibrated at $20^{\circ} \mathrm{C}$. When temperature is increased to $30^{\circ} \mathrm{C}$, then how much time does the clock lose or gain in one week ? $\left[\alpha_{\text {steel }}=1.2 \times 10^{-5}\left({ }^{\circ} \mathrm{C}\right)^{-1}\right]$
(a) $0.3628 \mathrm{~s}$
(b) $3.626 \mathrm{~s}$
(c) $362.8 \mathrm{~s}$
(d) $36.28 \mathrm{~s}$

Ajay Singhal

Numerade Educator

Problem 16

A uniform brass disc of radius $a$ and mass $m$ is set into spinning with angular speed $\omega_{0}$ about an axis passing through centre of disc and perpendicular to the plane of disc. If its temperature increases from $\theta_{1}{ }^{\circ} \mathrm{C}$ to $\theta_{2}^{\circ} \mathrm{C}$ without disturbing the disc, what will be its new angular speed ? (The coefficient of linear expansion of brass is $\alpha$ ).
(a) $\omega_{0}\left[1+2 \alpha\left(\theta_{2}-\theta_{1}\right)\right]$
(b) $\omega_{0}\left[1+\alpha\left(\theta_{2}-\theta_{1}\right)\right]$
(c) $\frac{\omega_{0}}{\left[1+2 \alpha\left(\theta_{2}-\theta_{1}\right)\right]}$
(d) None of these

Dheeraj Sharma

Numerade Educator

Problem 17

Two identical rods $A$ and $B$ are of equal lengths and at the same temperature. The rod $A$ is placed at smooth surface but $B$ is placed at rough surface. If the temperature of both are raised by the same amount, then :
(a) final length of $A$ is greater than that of $B$
(b) final length of both are same
(c) final length of $A$ is lesser than that of $B$
(d) none of the above

Ajay Singhal

Numerade Educator

Problem 18

Calculate the compressional force required to prevent the metallic rod of length $l \mathrm{~cm}$ and cross-sectional area $A \mathrm{~cm}^{2}$ when heated through $t^{\circ} \mathrm{C}$, from expanding along lengthwise. The Young's modulus of elasticity of the metal is $E$ and mean coefficient of linear expansion is $\alpha$ per degree celsius:
(a) EA\alphat
(b) $\frac{E \text { A\alphat }}{(1+\alpha t)}$
(c) $\frac{E A \alpha t}{(1-\alpha t)}$
(d) El\alphat

Ajay Singhal

Numerade Educator

Problem 19

A plate composed of welded sheets of aluminium and iron is connected to an electrical circuit as shown in fig. What will happen if a fairly strong current be passed through the circuit?
(a) Strip bends upward
(b) Strip bends downward
(c) Strip remains in its initial condition
(d) None of the above

Ajay Singhal

Numerade Educator

Problem 20

A steel rod of $30 \mathrm{~mm}$ diameter and $0.3 \mathrm{~m}$ long is Subjected to a tensile force $W$ kilo newton acting axially. The temperature of the rod raised through $80^{\circ} \mathrm{C}$ and total extension measured as $0.35 \mathrm{~mm}$. The value of $\mathrm{W}$ is:
$\left(Y_{\mathrm{s}}=2 \times 10^{5} \mathrm{~N} / \mathrm{mm}^{2}, \alpha_{5}=12 \times 10^{-6} /{ }^{\circ} \mathrm{C}\right)$
(a) $29.20$
(b) 40
(c) 50
(d) 12

Ajay Singhal

Numerade Educator

Problem 21

At temperature $T_{0}$, two metal strips of length $l_{0}$ and thickness $d$, is bolted so that their ends coincide. The upper strip is made up of metal $A$ and have coefficient of expansion $\alpha_{A}$ and lower strip is made up of metal $B$ with coefficient of expansion $\alpha_{B} \cdot\left(\alpha_{A}>\alpha_{B}\right)$. When temperature of their blastic strip is in-seased from $T_{0}$ to $\left(T_{0}+\Delta T\right)$, on strip become longer than the other and blastic strip is bend in the form of a circle as shown in fig. Calculate the radius of furvature $R$ of the strip:
(a) $R:=\frac{\left[2+\left(\alpha_{A}+\alpha_{B}\right) \Delta T\right] d}{2\left(\alpha_{A}-\alpha_{B}\right) \Delta T}$
(b) $R=\frac{\left[2-\left(\alpha_{A}+\alpha_{B}\right) \Delta T\right] d}{2\left(\alpha_{A}-\alpha_{B}\right) \Delta T}$
(c) $R=\frac{\left[2+\left(\alpha_{A}-\alpha_{B}\right) \Delta T\right] d}{2\left(\alpha_{A}-\alpha_{B}\right) \Delta T_{i}}$
(d) $R=\frac{\left[2-\left(\alpha_{A}-\alpha_{B}\right) \Delta T\right] d}{2\left(\alpha_{A}-\alpha_{B}\right) \Delta \mathcal{k}}$

Dheeraj Sharma

Numerade Educator

Problem 22

A cube of ice is placed on a bimetallic strip at room temperature as shown in the figure. What will happen if the upper strip is of iron and the lower strip is of copper?
(a) Ice moves downwards
(b) Ice moves upwasds
(c) Ice remains in rest
(d) None of the above

Ajay Singhal

Numerade Educator

Problem 23

A copper rod of length $l_{0}$ at $0^{\circ} \mathrm{C}$ is placed on smooth surface. The rod is heated up to $100^{\circ} \mathrm{C}$. The longitudinal strain developed is :
$(\alpha=$ coefficient of linear expansion)
(a) $\frac{100 l_{0} \alpha}{l_{0}+100 l_{0} \alpha}$
(b) $100 \alpha$
(c) zero
(d) none of these

Ajay Singhal

Numerade Educator

Problem 24

A steel rod of diameter $1 \mathrm{~cm}$ is clamped firmly at each end when its temperature is $25^{\circ} \mathrm{C}$ so that it cannot contract on cooling. The tension in the rod at $0^{\circ} \mathrm{C}$ is :
$\left(\alpha=10^{-5} /{ }^{\circ} \mathrm{C}, Y=2 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}\right)$
(a) $4000 \mathrm{~N}$
(b) $7000 \mathrm{~N}$
(c) $7400 \mathrm{~N}$
(d) $4700 \mathrm{~N}$

Ajay Singhal

Numerade Educator

Problem 25

Two metal rods are fixed end to end between two rigid supports, as shown in figure. Each rod is of length ' $T$ and area of cross-section is $A$. When the system is heated up, determine the condition when the junction between rods does not shift ? [Given: $Y_{1}$ and $Y_{2}$ are Young's modulus of materials of the rods, $\alpha_{1}$ and $\alpha_{2}$ are coefficients of linear expansion.]
(a) $\alpha_{1} Y_{2}=\alpha_{2} Y_{1}$
(b) $\alpha_{1} Y_{1}=\alpha_{2} Y_{2}$
(c) $\alpha_{1}=\alpha_{2}$
(d) $Y_{1}=Y_{2}$

Ajay Singhal

Numerade Educator

Problem 26

What will be the stress at $-20^{\circ} \mathrm{C}$, if a steel rod with a cross-sectional area of $150 \mathrm{~mm}^{2}$ is stretched between two fixed points? The tensile load at $20^{\circ} \mathrm{C}$ is $5000 \mathrm{~N}:$ (Assume $\alpha=11.7 \times 10^{-6} /{ }^{\circ} \mathrm{C}$ and $Y=200 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}$ )
(a) $12.7 \times 10^{6} \mathrm{~N} / \mathrm{m}^{2}$
(b) $1.27 \times 10^{6} \mathrm{~N} / \mathrm{m}^{2}$
(c) $127 \times 10^{6} \mathrm{~N} / \mathrm{m}^{2}$
(d) $0.127 \times 10^{6} \mathrm{~N} / \mathrm{m}^{2}$

Ajay Singhal

Numerade Educator

Problem 27

Two steel rods and copper rod of equal length $l_{0}$ and equal cross-sections are joined rigidly as shown. All the rods are in a state of zero tension at $0^{\circ} \mathrm{C}$. The temperature of system increases upto $30^{\circ} \mathrm{C}$, then :
(a) tensile force on either steel plate is half of copper plate
(b) the net expansion in copper plate is less than the thermal expansion of the copper plate
(c) the expansion in either steel plates is larger than thermal expansion in steel plates
(d) all of the above

Dheeraj Sharma

Numerade Educator

Problem 28

An equilateral triangle $A B C$ is formed by joining three rods of equal length and $D$ is the mid-point of $A B$. The coefficient of linear expansion for $A B$ is $\alpha_{1}$ and for $A C$ and $B C$ is $\alpha_{2}$. Find the relation between $\alpha_{1}$ and $\alpha_{2}$, if distance $D C$ remains constant for small changes in temperature
(a) $\alpha_{1}=\alpha_{2}$
(b) $\alpha_{1}=4 \alpha_{2}$
(c) $\alpha_{2}=4 \alpha_{1}$
(d) $\alpha_{1}=\frac{1}{2} \alpha_{2}$

Dheeraj Sharma

Numerade Educator

Problem 29

In an anisotropic medium, the coefficients of linear expansion of a solid are $\alpha_{1}, \alpha_{2}$ and $\alpha_{3}$ in three mutually perpendicular directions. The coefficient of volume expansion for the solid is
(a) $\alpha_{1}-\alpha_{2}+\alpha_{3}$
(b) $\frac{\alpha_{1}+\alpha_{2}+\alpha_{3}}{3}$
(c) $\alpha_{1}+\alpha_{2}+\alpha_{3}$
(d) none of these

Ajay Singhal

Numerade Educator

Problem 30

The density of a liquid at $0^{\circ} \mathrm{C}$ is $\rho_{0}$. The density of liquid at $0^{\circ} \mathrm{C}$ is : [volume expansion of liquid is $\gamma$ ]
(a) $\frac{\rho_{0}}{\left[1+\gamma\left(\theta_{2}-\theta_{1}\right)\right]}$
(b) $\rho_{0}\left[1+\gamma\left(\theta_{2}-\theta_{1}\right)\right]$
(c) $\rho_{0}\left[1+\gamma \theta_{2}\right]$
(d) none of these

Ajay Singhal

Numerade Educator

Problem 31

The coefficient of linear expansion of glass is $\alpha_{8}$ per ${ }^{\circ} \mathrm{C}$ and the cubical expansion of mercury is $\gamma_{m}$ per ${ }^{\circ} \mathrm{C}$. The volume of the bulb of a mercury thermometer at $0^{\circ} \mathrm{C}$ is $V_{0}$ and cross-section of the capillary is $A_{0}$. What is the. length of mercury column in capillary at $T^{\circ} \mathrm{C}$, if the mercury just fills the bulb at $0^{\circ} \mathrm{C}$ ?
(a) $\frac{V_{0} T\left(\gamma_{m}+3 \alpha_{p}\right)}{A_{0}\left(1+2 \alpha_{g} T\right)}$
(b) $\frac{V_{0} T\left(\gamma_{m}-3 \alpha_{Q}\right)}{A_{0}\left(1+2 \alpha_{g} T\right)}$
(c) $\frac{V_{0} T\left(\gamma_{m}+2 \alpha_{g}\right)}{A_{0}\left(1+3 \alpha_{g} T\right)}$
(d) $\frac{V_{0} T\left(\gamma_{m}-2 \alpha_{g}\right)}{A_{0}\left(1+3 \alpha_{\varphi} T\right)}$

Ajay Singhal

Numerade Educator

Problem 32

The bulk modulus of water is $2.1 \times 10^{9} \mathrm{~N} / \mathrm{m}^{2}$. The pressure required to increase the density of water by $0.1 \%$ is :
(a) $2.1 \times 10^{3} \mathrm{~N} / \mathrm{m}^{2}$
(b) $2.1 \times 10^{6} \mathrm{~N} / \mathrm{m}^{2}$
(c) $2.1 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}$
(d) $2.1 \times 10^{2} \mathrm{~N} / \mathrm{m}^{2}$

Ajay Singhal

Numerade Educator

Problem 33

At a temperature $t^{\circ} \mathrm{C}$, a liquid is completely filled in a spherical shell of copper. If $\Delta T$ increases temperature of the liquid and the shell, then the outward pressure $d P$ on the shell resulted from increase in temperature is given by: (Given, $K=$ Bulk modulus of the liquids, $\gamma=$ coefficient of volume expansion, $\alpha=$ coefficient of linear expansion of the material of the shell)
(a) $\frac{K}{2}(\gamma-3 \alpha) \Delta T$
(b) $K(3 \alpha-\gamma) \Delta T$
(c) $3 \alpha(K-\gamma) \Delta T$
(d) $\gamma(3 \alpha-K) \Delta T$

Dheeraj Sharma

Numerade Educator

Problem 34

A liquid when heated in a copper vessel and when heated in a silver vessel, the apparent coefficient of expansion is ' $C^{\prime}$ and ' $S^{\prime}$, respectively. If coefficients of linear expansion of copper is ' $A^{\prime}$, then coefficient of linear expansion of silver is :
(a) $\frac{C+S-3 A}{3}$
(b) $\frac{C+3 A-S}{3}$
(c) $\frac{3 A-S-C}{3}$
(d) $\frac{C+S+3 A}{3}$

Ajay Singhal

Numerade Educator

Problem 35

Using the following, data, at what temperature will the wood just sink in benzene?
Density of wood at $0^{\circ} \mathrm{C}=8.8 \times 10^{2} \mathrm{~kg} / \mathrm{m}^{3}$
Density of benzene at $0^{\circ} \mathrm{C}=9 \times 10^{2} \mathrm{~kg} / \mathrm{m}^{3}$
Cubical expansivity of wood $=1.5 \times 10^{-4} \mathrm{~K}^{-1}$ Cubical expansivity of benzene $=1.2 \times 10^{-3} \mathrm{~K}^{-1}$
(a) $27^{\circ} \mathrm{C}$
(b) $21.7^{\circ} \mathrm{C}$
(c) $31^{\circ} \mathrm{C}$
(d) $31.7^{\circ} \mathrm{C}$

Ajay Singhal

Numerade Educator

Problem 36

In a U-tube, a liquid is poured to a height $h^{\prime}$ in each arm. When left and right arms of the tube is heated to temperature $T_{1}$ and $T_{2}$ respectively, the height in each arm changes to $h_{1}$ and $h_{2}$ respectively. What is the relation between coefficients of volume expansion of liquid and heights, $h_{1}$ and $h_{2}$ ?
(a) $\gamma=\frac{h_{1}-h_{2}}{T_{1} h_{2}-T_{2} h_{1}}$
(b) $\gamma=\frac{h_{1}+h_{2}}{T_{1} h_{2}-T_{2} h_{1}}$
(c) $\gamma=\frac{h_{1}+h_{2}}{T_{1} h_{2}+T_{2} h_{1}}$
(d) $\gamma=\frac{h_{1}-h_{2}}{T_{1} h_{1}-T_{2} h_{2}}$

Ajay Singhal

Numerade Educator

Problem 37

A physicist says "a body contains 10 joule heat" but a physics learner says "this statement is correct only when the body is in liquid state". Mark correct option or options:
(a) physicist statement is correct
(b) physics learner's statement is correct
(c) both statements are correct
(d) both statements are wrong

Ajay Singhal

Numerade Educator

Problem 38

A sphere $A$ is placed at smooth table. An another sphere $B$ is suspended as shown in figure. Both spheres are identical in all respects. Equal quantity of heat is supplied to both spheres. All kinds of heat loss are neglected. The final temperatures of $A$ and $B$ are $T_{A}$ and $T_{B}$ respectively, then : (a) $T_{A}=T_{B}$
(b) $T_{A}>T_{B}$
(c) $T_{A}<T_{B}$
(d) none of these

Ajay Singhal

Numerade Educator

Problem 39

The resulting temperature when $20 \mathrm{~g}$ of boiling water is poured into an ice-cold brass vessel of mass $100 \mathrm{~g}$, is :
(specific heat $\left.=0.1 \mathrm{cal} / \mathrm{g}^{\circ} \mathrm{C}\right):$
(a) $66.66^{\circ} \mathrm{C}$
(b) $6.66^{\circ} \mathrm{C}$
(c) $0.66^{\circ} \mathrm{C}$
(d) $50^{\circ} \mathrm{C}$

Ajay Singhal

Numerade Educator

Problem 40

The ratio of thermal capacities of two spheres $A$ and $B$, if their diameters are in the ratio $1: 2$, densities in the ratio $2: 1$, and the specific heat in the ratio of $1: 3$, will be:
(a) $1: 6$
(b) $1: 12$
(c) $1: 3$
(d) $1: 4$

Ajay Singhal

Numerade Educator

Problem 41

In similar calorimeters, equal volumes of water and alcohol, when poured, take $100 \mathrm{~s}$. and 74 s respectively to cool from $50^{\circ} \mathrm{C}$ to $40^{\circ} \mathrm{C}$. If the thermal capacity of each calorimeter is numerically equal to volume of either liquid, then the specific heat capacity of alcohol is :
(Given: the relative density of alcohol as $0.8$ and specific heat capacity of water as $1 \mathrm{cal} / \mathrm{g} /{ }^{\circ} \mathrm{C}$ )
(a) $0.8 \mathrm{cal} / \mathrm{g}^{\circ} \mathrm{C}$
(b) $0.6 \mathrm{cal} / \mathrm{g}^{\circ} \mathrm{C}$
(c) $0.9 \mathrm{cal} / \mathrm{g}^{\circ} \mathrm{C}$
(d) $1 \mathrm{cal} / \mathrm{g}^{\circ} \mathrm{C}$

Ajay Singhal

Numerade Educator

Problem 42

The molar heat capacity of rock salt at low temperatures varies with temperature according to Debye's $T^{3}$ law". Thus, $C=k \frac{T^{3}}{\theta^{3}}$ where, $k=1940 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}, \theta=281 \mathrm{~K}$.
How much heat is required to raise the temperature of 2 moles of rock salt from $10 \mathrm{~K}$ to $50 \mathrm{~K}$ ?
(a) $800 \mathrm{~J}$
(b) $373 \mathrm{~J}$
(c) $273 \mathrm{~J}$
(d) None of these

Ajay Singhal

Numerade Educator

Problem 43

The specific heat of a substance at temperature $t{ }^{\circ} \mathrm{C}$ is $s=a t^{2}+b t+c .$ The amount of heat required to raise the temperature of $m \mathrm{~g}$ of the substance from $0^{\circ} \mathrm{C}$ to $t_{0}^{\circ} \mathrm{C}$, is :
(a) $\frac{m t_{0}^{2} a}{3}+\frac{b t_{0}^{2}}{2}+c t_{0}$
(b) $\frac{m t_{0}^{3} a}{3}+\frac{m b t_{0}^{2}}{2}+m c t_{0}$
(c) $\frac{m t_{0}^{3} a}{3}+\frac{m b t_{0}^{2}}{2}$
(d) none of these

Ajay Singhal

Numerade Educator

Problem 44

In above problem, average value of specific heat is:
(a) $\frac{a t_{0}^{3}}{3}+\frac{b t_{0}^{2}}{2}+c t_{0}$
(b) $\frac{a t_{0}}{3}+\frac{b t_{0}^{2}}{2}+c$
(c) $a t_{0}^{2}+b t_{0}+c$
(d) zero

Ajay Singhal

Numerade Educator

Problem 45

If rotation of the earth stopped suddenly then the rise in temperature of the earth, assume total rotational energy is converted into thermal energy, is: (specific heat of earth $=0.15$, radius of earth $=6400 \mathrm{~km}$ )
(a) $78.76^{\circ} \mathrm{C}$
(b) $6.876^{\circ} \mathrm{C}$
(c) $68.76^{\circ} \mathrm{C}$
(d) $0.6876^{\circ} \mathrm{C}$

Ajay Singhal

Numerade Educator

Problem 46

A drilling machine of $10 \mathrm{~kW}$ power is used to drill a bore in a small aluminium block of mass $8 \mathrm{~kg}$. If $50 \%$ of power is used up in heating the machine itself or lost to the surroundings then how much is the rise in temperature of the block in $2.5$ minutes? (Given: specific heat of aluminium $=0.91 \mathrm{~J} / \mathrm{g}^{\circ} \mathrm{C}$ )
(a) $103^{\circ} \mathrm{C}$
(b) $130^{\circ} \mathrm{C}$
(c) $105^{\circ} \mathrm{C}$
(d) $30^{\circ} \mathrm{C}$

Ajay Singhal

Numerade Educator

Problem 47

A thermally insulated piece of metal is heated under atmosphere by an electric current so that it receives electric energy at a constant power $P$. This leads to an increase of the absolute temperature $T$ of the metal with time $t$ as follows $T=a t^{1 / 4}$
Then the heat capacity $C_{p}$ is :
(a) $\frac{4 P T^{5}}{a^{4}}$
(c) $4 P T^{2}$
(b) $\frac{4 P T^{\overline{4}}}{a^{3}}$
(d) none of these

Ajay Singhal

Numerade Educator

Problem 48

A source of heat supplies heat at a constant rate to a solid cube. The variation of the temperature of the cube with the heat supplied is shown in the fig. The slope of the part $S T$ of the graph represents :
(a) the latent heat of the vapour
(b) the specific heat of the vapour
(c) the thermal capacity of the vapour
(d) the reciprocal of the thermal capacity

Ajay Singhal

Numerade Educator

Problem 49

The temperature at which phase transition occurs, depends on:
(a) pressure
(b) volume
(c) density
(d) mass

Ajay Singhal

Numerade Educator

Problem 50

Under some conditions, a material can be heated above or cooled below the normal phase change temperature without a phase change occurring. The resulting state :
(a) may be stable
(b) may be unstable
(c) must be stable
(d) must be unstable

Ajay Singhal

Numerade Educator

Problem 51

Water at $-10^{\circ} \mathrm{C}$ is present in a thermally insulated container. The ratio of mass of ice formed and initial mass of water, if a small crystal of ice is thrown into it, will be :
(a) $1 / 15$
(b) $1 / 17$
(c) $2 / 15$
(d) $1 / 8$

Ajay Singhal

Numerade Educator

Problem 52

It takes 20 minutes to melt $10 \mathrm{~g}$ of ice, when rays from the 'sun are focussed by a lens of diameter $5 \mathrm{~cm}$ on to a block of ice. The heat received from the sun on $1 \mathrm{~cm}^{2}$ per minute is : (Given: $L=80 \mathrm{k} \mathrm{cal} / \mathrm{kg}$ )
(a) $R=2.04 \mathrm{cal} / \mathrm{cm}^{2}-\mathrm{min}$
(b) $R=3.04 \mathrm{cal} / \mathrm{cm}^{2}-\mathrm{min}$
(c) $R=0.204 \mathrm{cal} / \mathrm{cm}^{2}-\min$ (d) $R=204 \mathrm{cal} / \mathrm{cm}^{2}-\mathrm{min}$

Ajay Singhal

Numerade Educator

Problem 53

If in $1.1 \mathrm{~kg}$ of water which is contained in a calorimeter of water equivalent $0.02 \mathrm{~kg}$ at $15^{\circ} \mathrm{C}$, steam at $100^{\circ} \mathrm{C}$ is passed, till the temperature of calorimeter and its contents rises to $80^{\circ} \mathrm{C}$. The mass of steam condensed in kilogram is:
(a) $0.131$
(b) $0.065$
(c) $0.260$
(d) $0.135$

Ajay Singhal

Numerade Educator

Problem 54

$5 \mathrm{~g}$ of water at $30^{\circ} \mathrm{C}$ and $5 \mathrm{~g}$ of ice at $-20^{\circ} \mathrm{C}$ are mixed together in a calorimeter. The water equivalent of calorimeter is negligible and specific heat and latent heat of ice are $0.5 \mathrm{cal} / \mathrm{g}^{\circ} \mathrm{C}$ and $80 \mathrm{cal} / \mathrm{g}$ respectively. The final temperature of the mixure is:
(a) $0^{\circ} \mathrm{C}$
(b) $-8^{\circ} \mathrm{C}$
(c) $-4^{\circ} \mathrm{C}$
(d) $2^{\circ} \mathrm{C}$

Ajay Singhal

Numerade Educator

Problem 55

In an energy recycling process, $X g$ of steam at $100^{\circ} \mathrm{C}$ becomes water at $100^{\circ} \mathrm{C}$ which converts $Y \mathrm{~g}$ of ice at $0^{\circ} \mathrm{C}$ into water at $100^{\circ} \mathrm{C}$. The ratio of $X / Y$ will be :
(a) $\frac{1}{3}$
(b) $\frac{2}{3}$
(c) 3
(d) 2

Ajay Singhal

Numerade Educator

Problem 56

At $30^{\circ} \mathrm{C}$, a lead bullet of $50 \mathrm{~g}$, is fired vertically upwards with a speed of $840 \mathrm{~m} / \mathrm{s}$. The specific heat of lead is $0.02 \mathrm{cal} / \mathrm{g}^{\circ} \mathrm{C}$. On returning to the starting level, it strikes to a cake of ice at $0^{\circ} \mathrm{C}$. The amount of ice melted is:
(Assume all the energy is spent in melting only)
(a) $62.7 \mathrm{~g}$
(b) $55 \mathrm{~g}$
(c) $52.875 \mathrm{~kg}$
(d) $52.875 \mathrm{~g}$

Ajay Singhal

Numerade Educator