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The SI unit for heat capacity is joule per kelvin.

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Important Questions on Thermal Properties of Matter

MEDIUM

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Specific Heat Capacity

Two different liquids of same mass are kept in two identical vessels, which are placed in a freezer that extracts heat from them at the same rate causing each liquid to transform into a solid. The schematic figure below shows the temperature T vs time t plot for the two materials. We denote the specific heat of materials in the liquid (solid) states to be $C_{L 1} (C_{S 1})$ and $C_{L 2} (C_{S 2})$ respectively.

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HARD

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Specific Heat Capacity

10.0 W

electrical heater is used to heat a container filled with

0.5 kg

of water. It is found that the temperature of the water and the container rise by

3 K

15

minutes. The container is then emptied, dried, and filled with

2 kg

of an oil. It is now observed that the same heater raises the temperature of the container-oil system by

2 K

20

minutes. Assuming no other heat losses in any of the processes, the specific heat capacity of the oil is

HARD

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Specific Heat Capacity

The figure below shows the variation of specific heat capacity ( $C$ ) of a solid as a function of temperature ( $T$ ). The temperature is increased continuously from $0$ to $500 K$ at a constant rate. Ignoring any volume change, the following statement (s) is (are) correct to a reasonable approximation.

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MEDIUM

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Specific Heat Capacity

Water of volume 2 L in a closed container is heated with a coil of 1 kW. While water is heated, the container loses energy at a rate of 160 J/s. In how much time will the temperature of water rise from 27^oC to 77^oC ? (Specific heat of water is 4.2 kJ/kg and that of the container is negligible).

EASY

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Specific Heat Capacity

4.0 g

of a gas occupies

22.4

liters at NTP. The specific heat capacity of the gas at constant volume is

5.0 J K^{- 1} m o l^{- 1}

. If the speed of sound in this gas at NTP is

952 m s^{- 1}

, then the heat capacity at constant pressure is

(Take gas constant

R = 8.3 J K^{- 1} m o l^{- 1}

)

HARD

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Specific Heat Capacity

1 kg

of ice at

- 20^{o} C

is mixed with

2 kg

of water at

90^{o} C

. Assuming that there is no loss of energy to the environment, what will be the final temperature of the mixture? (Assume latent heat of ice

= 334.4 kJ {(kg)}^{- 1}

, specific heat of water and ice are

4.18 kJ {(kg - K)}^{- 1}

and

2.09 kJ {(kg - K)}^{- 1}

, respectively.)

EASY

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Specific Heat Capacity

Two moles of oxygen is mixed with eight moles of helium. The effective specific heat of the mixture at constant volume is

MEDIUM

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Specific Heat Capacity

When

M_{1}

gram of ice at

- 10^{o} C

(specific heat

= 0.5 c a l g^{- 1} ℃^{- 1}

) is added to

M_{2}

gram of water at

50^{o} C,

finally no ice is left and the water is at

0^{o} C

. The value of latent heat of ice, in

c a l g^{- 1}

is:

MEDIUM

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Specific Heat Capacity

An experiment takes

10 \min

to raise the temperature of water in a container from

0^{o} C

100^{o} C

and another

55 \min

to convert it totally into steam by a heater supplying heat at a uniform rate. Neglecting the specific heat of the container and taking specific heat of the water to be

1 cal {(g^{\circ} C)}^{- 1}

, the heat of vaporization according to this experiment will come out to be:

EASY

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Specific Heat Capacity

Two identical bodies are made of a material for which the heat capacity increases with temperature. One of these is at

100^{o} C

, while the other one is at

0^{o} C

. If the two bodies are brought into contact, then assuming no heat loss, the final common temperature is

EASY

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Specific Heat Capacity

200 g

water is heated from

40^{o} C

60^{o} C

. Ignoring the slight expansion of water, the change in its internal energy is close to (Given specific heat of water

= 4184

J {kg}^{- 1} K^{- 1}

MEDIUM

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Specific Heat Capacity

An unknown metal of mass

192 g

heated to a temperature of

100 ° C

was immersed into a brass calorimeter of mass

128 g

containing

240 g

of water at a temperature of

8.4 ° C .

Calculate the specific heat of the unknown metal if water temperature stabilizes at

21.5 ° C .

(

Specific heat of brass is

394 J {kg}^{- 1} K^{- 1})

HARD

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Specific Heat Capacity

Three containers

C_{1}, C_{2}

and

C_{3}

have water at different temperatures. The table below shows the final temperature

T

when different amounts of water (given in liters) are taken from each container and mixed (assume no loss of heat during the process)

$C_{1}$	$C_{2}$	$C_{3}$	$T$
$1 l$	$2 l$	$- -$	$60^{o} C$
$- -$	$1 l$	$2 l$	$30^{o} C$
$2 l$	$- -$	$1 l$	$60^{o} C$
$1 l$	$1 l$	$1 l$	$θ$

The value of

θ

(in

^{o} C

to the nearest integer) is___________

HARD

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Specific Heat Capacity

20 g

bullet whose specific heat is,

5000 J {kg}^{- 1} {}^{\circ}C^{- 1}

and moving at,

2000 m s^{- 1}

plunges into a

1.0 kg

block of wax whose specific heat is,

3000 J {kg}^{- 1} {}^{\circ}C^{- 1}

. Both bullet and wax are at,

25 ° C

and assume that

(i)

the bullet comes to rest in the wax and

(ii)

all its kinetic energy goes into heating the wax. The thermal temperature of the wax in,

{}^{\circ}C

is close to.

HARD

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Specific Heat Capacity

A massless spring

(k = 800 N / m),

attached with a mass

(500 g)

is completely immersed in

1 k g

of water. The spring is stretched by

2 c m

and released so that it starts vibrating. What would be the order of magnitude of the change in the temperature of water when the vibrations stop completely? (Assume that the water container and spring receive negligible heat and specific heat of mass

= 400 J / k g K,

specific heat of water

= 4184 J / k g K

)

MEDIUM

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Specific Heat Capacity

When heat

Q

is supplied to a diatomic gas of rigid molecules, at constant volume its temperature increases by

∆ T

. The heat required to produce the same change in temperature, at a constant pressure is:

MEDIUM

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Specific Heat Capacity

Steam at

100^{o} C

is passed into

20 g

of water at

10^{o} C .

When water acquires a temperature of

80^{o} C,

the mass of water present will be:
[Take specific heat of water

= 1 c a l g^{- 1 o} C^{- 1}

and latent heat of steam

= 540 c a l g^{- 1}]

MEDIUM

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Specific Heat Capacity

A copper ball of mass

100 g

is at a temperature

T

. It is dropped in a copper calorimeter of mass

100 g,

filled with

170 g

of water at room temperature. Subsequently, the temperature of the system is found to be

75 ° C

T

is given by:
(Given: room temperature

= 30 ° C

, specific heat of copper

= 0.1 cal g^{- 1} ° C^{- 1}

)

MEDIUM

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Specific Heat Capacity

For a diatomic ideal gas in a closed system, which of the following plots does not correctly describe the relation between various thermodynamic quantities?

HARD

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Specific Heat Capacity

A water cooler of storage capacity

120

litres can cool water at constant rate of

P

W

. In a closed circulation system (as shown schematically in the figure), the water from the cooler is used to cool an external device that generates constantly

3

kW

of heat (thermal load). The temperature of water fed into the device can not exceed

30^{o} C

and the entire stored

120

litres of water is initially cooled to

10^{o} C

. The entire system is thermally insulated. The minimum value of

P

(in

W

) for which the device can be operated for

3

hours is:

(Specific heat of water is

4.2 kJ

k g^{- 1} K^{- 1}

and the density of water is

1000 kg m^{- 3}

)

The SI unit for heat capacity is joule per kelvin.

Important Questions on Thermal Properties of Matter

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