An insulator container contains \(4\) moles of an ideal diatomic gas at a temperature \(T.\) If heat \(Q\) is supplied to this gas, due to which \(2\) moles of the gas are dissociated into atoms, but the temperature of the gas remains constant, then:
1. \(Q=2RT\)
2. \(Q=RT\)
3. \(Q=3RT\)
4. \(Q=4RT\)

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

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 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: \(\gamma = 1.5\)]

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

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

In the \(P\text-V\) graph shown for an ideal diatomic gas, the change in the internal energy is: