MEDIUM

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In a certain experiment, liquid helium at an initial temperature of $1 K$ is to be further cooled by bringing it into contact with a paramagnetic salt which is initially at temperature $T_{0}$ . The heat capacity of liquid helium is expressed as $C_{h} = a T^{3} (a = 128 \times 10^{- 4} J \cdot K^{- 4})$ and that of salt is expressed as $C_{s} = b T^{- 2} (b = 15 \times 10^{- 4} J . K)$ . Assume that the mixture is thermally and mechanically isolated and no work is done during the process. If the final temperature of the system is $0.5 K$ , the initial temperature $T_{0}$ of the salt is

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Important Questions on Thermal Properties of Matter

HARD

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Principle of Calorimetry

A metallic block of mass

20 kg

is dragged with a uniform velocity of

0.5 {ms}^{- 1}

on a horizontal table for

2.1 s

. The coefficient of static friction between the block and the table is

0.10

. What will be the maximum possible rise in temperature of the metal block, if the specific heat of the block is

0.1 CGS

unit? Assume

g = 10 {ms}^{- 2}

and uniform rise in temperature throughout the whole block. [Ignore absorption of heat by the table]

MEDIUM

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Principle of Calorimetry

15 kW

drilling machine is used to drill a bore in a small aluminium block of mass

10 kg

. Assuming

50 %

power is used up in heating the machine itself or lost to the surroundings, then the rise in temperature of the block in

2

minutes is

(

Specific heat capacity of aluminium

= 0.91 J g^{- 1} ° C^{- 1}

)

HARD

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Principle of Calorimetry

The water equivalent of a calorimeter is

10 g

and it contains

50 g

of water at

15 ° C

. Some amount of ice, initially at

- 10 ° C

is dropped in it and half of the ice melts till equilibrium is reached. What was the initial amount of ice that was dropped (when specific heat of ice

= 0.5

cal

{gm}^{- 1} {}^{\circ}C^{- 1},

specific heat of water

= 1.0

cal

{gm}^{- 1 \circ} C^{- 1}

and latent heat of melting of ice

= 80

cal

{gm}^{- 1}

HARD

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Principle of Calorimetry

A coffee maker makes coffee by passing steam through a mixture of coffee powder, milk and water. If the steam is mixed at the rate of

50 g

per minute in a mug containing

500 g

of mixture, then it takes about

t_{0}

seconds to make coffee at

70 ° C

when the initial temperature of the mixture is

25 ° C

. The value of

t_{0}

is close to (ratio of latent heat of evaporation to specific heat of water is

540 ° C

and specific heat of the mixture can be taken to be the same as that of water)

MEDIUM

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Principle of Calorimetry

An aluminium piece of mass

50 g

initially at

300 ° C

is dipped quickly and taken out of

1 kg

of water, initially at

30 ° C .

If the temperature of the aluminium piece immediately after being taken out of the water is found to be

160 ° C,

what is the temperature of the water? Then, specific heat capacities of aluminium and water are

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

and

4200 J {kg}^{- 1} K^{- 1}

, respectively.

HARD

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Principle of Calorimetry

An earthen pitcher used in summer cools water in it essentially by evaporation of water from its porous surface. If a pitcher carries

4 kg

of water and the rate of evaporation is

20 g

per hour, temperature of water in it decreases by

Δ T

in two hours. The value of

Δ T

is close to (ratio of latent heat of evaporation to specific heat of water is

540 ° C

)

HARD

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Principle of Calorimetry

Two identical blocks of ice move in opposite directions with equal speed and collide with each other. What will be the minimum speed required to make both the blocks melt completely, if the initial temperatures of the blocks were $- 8 ° C$ each? (Specific heat of ice is $2100 J {kg}^{- 1} K^{- 1}$ and latent heat of fusion of ice is $3.36 \times 10^{5} J {kg}^{- 1})$

MEDIUM

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Principle of Calorimetry

How much time will a heater take to increase the temperature of

100 g

water by

50 ° C

, if the resistance of heating coil is

484 Ω

and the supply voltage is

220 V AC

HARD

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Principle of Calorimetry

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>Principle of Calorimetry

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:

HARD

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Principle of Calorimetry

A heater supplying constant power

P

watts is switched ON at time

t = 0 \min

to raise the temperature of a liquid kept in a calorimeter of negligible heat capacity. A student records the temperature of the liquid

T (t)

at equal time intervals. A graph is plotted with

T (t)

on the

Y

-axis versus

t

on the

X

-axis. Assume that there is no heat loss to the surroundings during heating. Then,

EASY

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Principle of Calorimetry

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

MEDIUM

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Principle of Calorimetry

The temperature of equal masses of three different liquids

x, y

and

z

are

10 ° C, 20 ° C

and

30 ° C

respectively. The temperature of mixture when

x

is mixed with

y

16 ° C

and that when

y

is mixed with

z

26 ° C

. The temperature of mixture when

x

and

z

are mixed will be :

HARD

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Principle of Calorimetry

When

100 g

of boiling water at

100 ° C

is added into a calorimeter containing

300 g

of cold water at

10 ° C

, temperature of the mixture becomes

20 ° C

. Then, a metallic block of mass

1 kg

10 ° C

is dipped into the mixture in the calorimeter. After reaching thermal equilibrium, the final temperature becomes

19 ° C .

What is the specific heat of the metal in CGS unit ?

EASY

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Principle of Calorimetry

1 gm

of ice at,

0 ° C

is mixed with,

2 gm

of water at

90 ° C

. Find the final temperature (specific heat capacity of water,

= 1 cal {(gm ° C)}^{- 1}

and latent heat of fusion of ice

=

80 cal {(gm)}^{- 1}

)

EASY

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Principle of Calorimetry

Ice in a freezer is at

- 7 ° C . 100 g

of this ice is mixed with

200 g

of water at

15 ° C

. Take the freezing temperature of water to be

0 ° C

, the specific heat of ice equal to

2.2 J / g ° C,

specific heat of water equal to

4.2 J / g ° C

and the latent heat of ice equal to

335 J / g

.
Assuming no loss of heat to the environment, the mass of ice in the final mixture is closest to

EASY

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Principle of Calorimetry

The SI unit of mechanical equivalent of heat is

MEDIUM

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Principle of Calorimetry

Two taps supply water to a container, one at the temperature of

20 ° C

at the rate of

2 kg / minute

and another at

80 ° C

at the rate of

1 kg / minute

. If the container gets water from the two taps simultaneously for 10 minutes, then the temperature of water in the container is

MEDIUM

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Principle of Calorimetry

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>Principle of Calorimetry

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})

Important Questions on Thermal Properties of Matter

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