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*Answer can only contain numeric values

QUESTION: 1

5000J of heat are added to two moles an ideal monoatomic gas, initially at a temperature of 500K, while the gas performs 7500J of work. What is the final temperature of the gas ? (in Kelvin)

Solution:

ΔU = ΔQ – ΔW = 5000 - 7500

ΔU = –2500 J

⇒ ΔT = –100 K

⇒ T = 500 - 100 = 400 K

The correct answer is: 400

*Answer can only contain numeric values

QUESTION: 2

For a diatomic ideal gas near room temperature, what fraction of heat supplied is available for external work if gas is expanded at constant pressure

Solution:

In the process of expansion at constant pressure p, assuming that the volume increases from V_{1} to V_{2} and temperature change from T_{1} to T_{2} , we have

pV_{1} = nRT_{1}

pV_{2} = nRT_{2}

In this process, the work done by the system on the outside world is W = p(V_{2} -V_{1} )= nRΔT and increase in internal energy of the system is

ΔU = C_{v}ΔT

∴

The correct answer is: 0.286

*Answer can only contain numeric values

QUESTION: 3

A gas has pressure p and volume V. It is now compressed adiabatically to 1/32 times the original volume. If (32)^{1.4} = 128, the final pressure in terms of p is

Solution:

For an adiabatic process,

⇒

⇒ p = (32)^{1.4} p

⇒ p_{1} = 128p.

The correct answer is: 128

*Answer can only contain numeric values

QUESTION: 4

1cm^{3} of water at its boiling point absorbs 540 calories of heat to become steam with a volume of 1671 cm^{3}. If the atmospheric pressure is 1.013 × 10^{5} N/m^{2} and mechanical equivalent of heat = 4.19 J/calorie, the energy spent in this process in overcoming intermolecular forces is (in calories)

Solution:

Energy spent in overcoming intermolecular forces

ΔU = ΔQ – ΔW

= ΔQ – p(V_{2} – V_{1})

= 500cal.

The correct answer is: 500

*Answer can only contain numeric values

QUESTION: 5

An ideal gas at 27ºC is compressed adiabatically to 8/27 of its original volume. If then the rise in temperature (in Kelvin) is

Solution:

For adiabatic process = constant

⇒

T_{2} = 675K

ΔT = 675–300

= 375K

The correct answer is: 375

*Answer can only contain numeric values

QUESTION: 6

Two systems with heat capacities 100cal/gm-K and 200cal/gm-K interact thermally and come to a common temperature 400K. If the initial temperature of system 1 is 500K, what was the initial temperature of systems (in Kelvin) scale

Solution:

Let initial temperature of system 2 is T_{2}. According to conservation of energy, we know that heat released from one system is equal to the heat absorbed by the other system, i.e.

C_{1} (T_{f} – T_{1} ) = C_{2} (T_{2} –T_{f} )

= –50+400

T_{2} = 350K

The correct answer is: 350

*Answer can only contain numeric values

QUESTION: 7

During an adiabatic processes, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio Cp /C_{V} for the gas is

Solution:

But for an adiabatic processes,

⇒

⇒

The correct answer is: 1.5

*Answer can only contain numeric values

QUESTION: 8

When an ideal gas is heated under constant pressure, then what percentage of given heat energy will be utilized in doing external work?

Solution:

∴ Percentage energy utilized in doing external work =

The correct answer is: 40

*Answer can only contain numeric values

QUESTION: 9

5 mole of hydrogen gas is heated from 30ºC to 60ºC at constant pressure. Heat given to the gas is in calories (given R = 2cal/mole-ºC)

Solution:

= 1050 calories

The correct answer is: 1050

*Answer can only contain numeric values

QUESTION: 10

Three liquids with masses m_{1}, m_{2}, m_{3} are thoroughly mixed. If their specific heats are C_{1}, C_{2} and C_{3} and their temperature T_{1}, T_{2}, T_{3}, then the temperature of the mixture is given that

Solution:

Let the final temperature be T K. Total heat supplied by 3 liquids in coming down to

Total heat used by three liquids in raising temperature from 0º to TºC

from (1) & (2),

⇒

T = 558.8K

The correct answer is: 558.8

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