The Carnot cycle (reversible) of gas is represented by a pressure-volume curve as shown in the figure. Consider the following statements:

I.	The area \(ABCD\) = The work done on the gas
II.	The area \(ABCD\) = The net heat absorbed
III.	The change in the internal energy in the cycle = \(0\)

Which of the statement(s) given above is/are correct?

             

1.	I only	2.	II only
3.	II and III	4.	I, II, and III

Which one of the following is correct for one complete cycle of a thermodynamic process on a gas as shown in the \((P-V)\) diagram?

A cyclic process for \(1\) mole of an ideal gas is shown in the \(V\text-T\) diagram. The work done in \(AB, BC\) and \(CA\) respectively is:

A monoatomic gas is supplied with the heat \(Q\) very slowly, keeping the pressure constant. The work done by the gas will be: 
1. \({2 \over 3}Q\)
2. \({3 \over 5}Q\)
3. \({2 \over 5}Q\)
4. \({1 \over 5}Q\)

A closed hollow insulated cylinder is filled with gas at \(0^{\circ}\mathrm{C}\) and also contains an insulated piston of negligible weight and negligible thickness at the middle point. The gas on one side of the piston is heated to \(100​​^{\circ}\mathrm{C}\). If the piston moves 5 cm, the length of the hollow cylinder will be:
1. 13.65 cm
2. 27.3 cm
3. 38.6 cm
4. 64.6 cm

When an ideal diatomic gas is heated at constant pressure, the fraction of the heat energy supplied which increases the internal energy of the gas is:

In a Carnot engine, when \(T_2=0^\circ \mathrm{C}\) and \(T_1=200^\circ \mathrm{C},\) its efficiency is \(\eta_1\) and when \(T_1=0^\circ \mathrm{C}\) and \(T_2=-200^\circ \mathrm{C},\) its efficiency is \(\eta_2.\) What is the value of \(\frac{\eta_1}{\eta_2}?\)

In a cyclic process, the internal energy of the gas:

One mole of an ideal gas at an initial temperature of T K does 6R joules of work adiabatically. If the ratio of specific heats of this gas at constant pressure and at constant volume is 5/3, the final temperature of the gas will be: