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

An ideal gas of mass m in a state A goes to another state B via three different processes as shown in figure. If Q₁, Q₂ and Q₃ denote the heat absorbed by the gas along the three paths, then -

(1) Q₁ < Q₂ < Q₃

(2) Q₁ < Q₂ = Q₃

(3) Q₁ = Q₂ > Q₃

(4) Q₁ > Q₂ > Q₃

A thermodynamic process is shown in the figure. The pressures and volumes corresponding to some points in the figure are : $P_A=3\times {10}^{4}Pa,P_B=8\times {10}^{4}Pa$ and $V_A=2\times {10}^{-3}{m}^3,V_D=5\times {10}^{-3}{m}^3$. In process AB, 600 J of heat is added to the system and in process BC, 200 J of heat is added to the system. The change in internal energy of the system in process AC would be 

(1) 560 J

(2) 800 J

(3) 600 J

(4) 640 J

P-V plots for two gases during adiabatic process are shown in the figure. Plots 1 and 2 should correspond respectively to -

(1) He and O₂

(2) O₂ and He

(3) He and Ar

(4) O₂ and N₂