If an ideal gas undergoes two processes at constant volumes \(V_1~\text{and}~V_2\) as shown in the pressure-temperature \((P\text-T)\) diagram, then:

             
1. \(V_1= V_2\)
2. \(V_1> V_2\)
3. \(V_1< V_2\)
4. \(V_1\ge V_2\)

The internal energy of an ideal gas increases in:

1. Adiabatic expansion

2. Adiabatic compression

3. Isothermal expansion

4. Isothermal compression

A refrigerator whose coefficient of performance is 5 extracts heat from the cooling chamber at a rate of 250 J per cycle. For refrigeration, the work done per cycle is:

1. 150 J

2. 200 J

3. 100 J

4. 50 J

\(0.04\) mole of an ideal monatomic gas is allowed to expand adiabatically so that its temperature changes from \(800~\text{K}\) to \(500~\text{K}\). The work done during expansion is nearly equal to:

Which of the following is true for the molar heat capacity of an ideal gas?

A heat engine is working between 200 K and 400 K. The efficiency of the heat engine may be:

1. 20%

2. 40%

3. 50%

4. All of these

In the cyclic process shown in the pressure-volume \((P-V)\) diagram, the change in internal energy is equal to:

1. $\pi {\left(\frac{{\mathrm{P}}_2-{\mathrm{P}}_1}{2}\right)}^2$

2. $\mathrm{\pi }{\left(\frac{{\mathrm{V}}_2-{\mathrm{V}}_1}{2}\right)}^2$

3. $\frac{\mathrm{\pi }}{4}({\mathrm{P}}_2-{\mathrm{P}}_1)({\mathrm{V}}_2-{\mathrm{V}}_1)$

4. zero

If a refrigerator extracts heat 'a' from the cold reservoir and 'b' is the heat released from the hot reservoir, then the work done on the refrigerant (system) is:

1. a + b

2. $\mathrm{a}-\mathrm{b}$

3. a

4. $\mathrm{b}-\mathrm{a}$