The initial pressure and volume of a gas are \(P\) and \(V\), respectively. First, it is expanded isothermally to volume \(4V\) and then compressed adiabatically to volume \(V\). The final pressure of the gas will be: [Given: \(\gamma = 1.5\)]

1.	\(P\)	2.	\(2P\)
3.	\(4P\)	4.	\(8P\)

A reversible engine converts one-sixth of the heat input into work. When the temperature of the sink is reduced by \(62^{\circ}\mathrm{C}\), the efficiency of the engine is doubled. The temperatures of the source and sink are: 
1. \(80^{\circ}\mathrm{C}, 37^{\circ}\mathrm{C}\)
2. \(95^{\circ}\mathrm{C}, 28^{\circ}\mathrm{C}\)
3. \(90^{\circ}\mathrm{C}, 37^{\circ}\mathrm{C}\)
4. \(99^{\circ}\mathrm{C}, 37^{\circ}\mathrm{C}\)

An ideal gas is taken from point A to point B, as shown in the P-V diagram. The work done in the process is:

       
1. $(P_A-P_B)(V_B-V_A)$
2. $\frac{1}{2}(P_B-P_A)(V_B+V_A)$
3. $\frac{1}{2}(P_B-P_A)(V_B-V_A)$
4. $\frac{1}{2}(P_B+P_A)(V_B-V_A)$

If the temperature of the source and the sink in the heat engine is at 1000 K & 500 K respectively, then the efficiency can be:
1. 20%
2. 30%
3. 50%
4. All of these

In an adiabatic process, the graph for work done versus change of temperature ∆T will be:

1.		2.
3.		4.

If n moles of an ideal gas is heated at a constant pressure from 50°C to 100°C, the increase in the internal energy of the gas will be: \(\left(\frac{C_{p}}{C_{v}} = \gamma\   and\   R = gas\   constant\right)\)

In the P-V graph shown for an ideal diatomic gas, the change in the internal energy is:
                                
1. \(\frac{3}{2}P(V_2-V_1)\)
2. \(\frac{5}{2}P(V_2-V_1)\)
3. \(\frac{3}{2}P(V_1-V_2)\)
4. \(\frac{7}{2}P(V_1-V_2)\)

Two Carnot engines x and y are working between the same source temperature \(T_1\) and the same sink temperature \(T_2\)${\mathrm{}}_{}$. If the temperature of the source in Carnot engine x is increased by \(\Delta T\), and in the Carnot engine y, the temperature of the sink is increased by\(\Delta T\), then the efficiency of x and y becomes \(\eta_\mathrm x\)${\mathrm{}}_{}$ and\(\eta_\mathrm y\)${\mathrm{}}_{}$. Then:

Two Carnot engines A and B are operated in succession. The first one, A receives heat from a source at \(T_1=800\) K and rejects to sink at \(T_2\) K. The second engine, B, receives heat rejected by the first engine and rejects to another sink at \(T_3=300\) K. If the work outputs of the two engines are equal, then the value of \(T_2\) will be:

The volume of air (diatomic) increases by \(5\%\) in its adiabatical expansion. The percentage decrease in its pressure will be: