An ideal gas expands isothermally from a volume V₁ to V₂ and then compressed to original volume V₁ adiabatically. Initial pressure is P₁ and final pressure is P₃. The total work done is W. Then -

(1) $P_3>P_1,W>0$

(2) $P_3<P_1,W<0$

(3) $P_3>P_1,W<0$

(4) $P_3=P_1,W=0$

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:

The temperature of a hypothetical gas increases to $\sqrt{2}$ times when compressed adiabatically to half the volume. Its equation can be written as

(1) PV^3/2 = constant

(2) PV^5/2 = constant

(3) PV^7/3 = constant

(4) PV^4/3 = constant

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:

Two samples A and B of a gas initially at the same pressure and temperature are compressed from volume V to V/2 (A isothermally and B adiabatically). The final pressure of A is 

(1) Greater than the final pressure of B

(2) Equal to the final pressure of B

(3) Less than the final pressure of B

(4) Twice the final pressure of B

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 thermally insulated rigid container contains an ideal gas heated by a filament of resistance 100 Ω through a current of 1A for 5 min . Then change in internal energy is -

(1) 0 kJ

(2) 10 kJ

(3) 20 kJ

(4) 30 kJ

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. \(99^{\circ}\mathrm{C}, 37^{\circ}\mathrm{C}\)

The P-V diagram shows seven curved paths (connected by vertical paths) that can be followed by a gas. Which two of them should be parts of a closed cycle if the net work done by the gas is to be at its maximum value ?

(1) ac

(2) cg

(3) af

(4) cd