NCERT Class 11 Physics Solutions: Chapter 12 – Thermodynamics-Part 2

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Question 12.4:

A cylinder with a movable piston contains 3 moles of hydrogen at standard temperature and pressure. The walls of the cylinder are made of a heat insulator, and the piston is insulated by having a pile of sand on it. By what factor does the pressure of the gas increase if the gas is compressed to half its original volume?

Answer:

The cylinder is completely insulated from its surroundings. As a result, no heat is exchanged between the system (cylinder) and its surroundings. Thus, the process is adiabatic.

Initial pressure inside the cylinder

Final pressure inside the cylinder

Initial volume inside the cylinder

Final volume inside the cylinder

Ratio of specific heats,

For an adiabatic process, we have:

The final volume is compressed to half of its initial volume.

Hence, the pressure increases by a factor of

Question 12.5:

In changing the state of a gas adiabatically from an equilibrium state to another equilibrium state , an amount of work equal to is done on the system. If the gas is taken from state to via a process in which the net heat absorbed by the system is , how much is the net work done by the system in the latter case? (Take)

Answer:

The work done on the system while the gas changes from state to state s This is an adiabatic process. Hence, change in heat is zero.

(Since the work is done on the system)

From the first law of thermodynamics, we have:

Where,

Change in the internal energy of the gas

When the gas goes from state to state via a process, the net heat absorbed by the system is:

Heat absorbed,

Therefore, of work is done by the system.

Question 12.6:

Two cylinders and of equal capacity are connected to each other via a stopcock. contains a gas at standard temperature and pressure is completely evacuated. The entire system is thermally insulated. The stopcock is suddenly opened.

Answer the following:

a) What is the final pressure of the gas in

b) What is the change in internal energy of the gas?

c) What is the change in the temperature of the gas?

d) Do the intermediate states of the system (before settling to the final equilibrium state) lie on its surface?

Answer:

The d in :

Explanation:

The volume available to the gas is doubled as soon as the stopcock between cylinders is opened. Since volume is inversely proportional to pressure, the pressure will decrease to one-half of the original value. Since the initial pressure of the gas is 1 atm, the pressure in each cylinder will be .

The change in internal energy of the gas: Zero

Explanation:

The internal energy of the gas can change only when work is done by or on the gas. Since in this case no work is done by or on the gas, the internal energy of the gas will not change.

the change in the temperature of the gas: Zero

Explanation:

Since no work is being done by the gas during the expansion of the gas, the temperature of the gas will not change at all.

The intermediate states of the system (before settling to the final equilibrium state) lie on its surface: No

Explanation:

C:\Users\Office1\Desktop\mathamatics\pvtgast.gif

Figure Shown the P-V-T Surface

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The given process is a case of free expansion. It is rapid and cannot be controlled. The intermediate states do not satisfy the gas equation and since they are in no equilibrium states, they do not lie on the P-V-T surface of the system.