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The specific heat capacity of a metal at low temperature ( $T$ ) is given as $C_{p} (k J K^{- 1} k g^{- 1}) = 32 {(\frac{T}{400})}^{3} .$ A 100 g vessel of this metal is to be cooled from 20 K to 4 K by a special refrigerator operating at room temperature $(27 ℃) .$ The amount of work required to cool the vessel is

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Important Questions on Thermal Properties of Matter

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}

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.

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

The specific heat of water

= 4200 J

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

and the latent heat of ice

= 3.4 \times 10^{5} J

{kg}^{- 1}

100 g

of ice at

0^{o} C

is placed in

200 g

of water at

25^{o} C

. The amount of ice that will melt as the temperature of water reaches

0^{o} C

is close to (in grams)

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}

)

EASY

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

A calorimeter of water equivalent

20 g

contains

180 g

of water at

25 ° C

{}^{'}m^{'}

' grams of steam at

100 ° C

is mixed in it till the temperature of the mixture is

31 ° C

. The value of

m

is close to (Latent heat of water

= 540 cal g^{- 1}

, specific heat of water

= 1 cal g^{- 1 °} C^{- 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

The specific heat capacity of body depends on

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

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

Steam at

100 ° C

is passed into

1.1 kg

of water contained in a calorimoter of water equivalent to

0.2 kg

15 ° C

till the temperature of the calorimeter and its contents rises to

80 ° C

. The mass of steam condensed (in

kg

) is

EASY

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

Ice is used in a cooler in order to cool its contents. Which of the following will speed up the cooling process?

HARD

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

A gas has molar heat capacity

C = 37.55 J {mol}^{- 1} K^{- 1}

, in this process

p T =

constant. The number of degree of freedom of the molecule of gas is

HARD

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

A current carrying wire heats a metal rod. The wire provides a constant power

(P)

to the rod. The metal rod is enclosed in an insulated container. It is observed that the temperature

(T)

in the metal rod changes with time

(t)

as:

T (t) = T_{0} (1 + β t^{\frac{1}{4}})

, where

β

is a constant with appropriate dimension while

T_{0}

is a constant with dimension of temperature. The heat capacity of the metal is:

MEDIUM

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

A horizontal fire hose with a nozzle of cross-sectional area $\frac{5}{\sqrt{21}} \times 10^{- 3} m^{2}$ delivers a cubic metre of water in $10 s .$ What will be the maximum possible increase in the temperature of water while it hits a rigid wall (neglecting the effect of gravity)?

MEDIUM

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

Due to cold weather, a $1 m$ water pipe of cross-sectional area $1 {cm}^{2}$ is filled with ice at $- 10 ° C .$ Resistive heating is used to melt the ice. Current of $0.5 A$ is passed through $4 kΩ$ resistance. Assuming that all the heat produced is used for melting, what is the minimum time required?

(Given latent heat of fusion for water/ice $= 3.33 \times 10^{5} J {kg}^{- 1},$ specific heat of ice $= 2 \times 10^{3} J {kg}^{- 1} ° C^{- 1}$ and density of ice $= 10^{3} kg m^{- 3})$

EASY

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

Two identical systems, with heat capacity at constant volume that varies as

C_{v} = b T^{3}

(where

b

is a constant) are thermally isolated. Initially, one system is at a temperature

100 K

and the other is at

200 K

. The systems are then brought to thermal contact and the combined system is allowed to reach thermal equilibrium. The final temperature (in

K

) of the combined system will be

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.

Question Image

MEDIUM

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

A thin paper cup filled with water does not catch fire when placed over a flame. This is because

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:

The specific heat capacity of a metal at low temperature (T) is given as CpkJK-1kg-1=32T4003. A 100 g vessel of this metal is to be cooled from 20 K to 4 K by a special refrigerator operating at room temperature 27℃. The amount of work required to cool the vessel is

Important Questions on Thermal Properties of Matter

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