The pressure-temperature (P-T) graph for two processes, A and B, in a system is shown in the figure. If ${\mathrm{W}}_1$ and ${\mathrm{W}}_2$ are work done by the gas in process A and B respectively, then:

      

1. ${\mathrm{W}}_1$ = ${\mathrm{W}}_2$

2. ${\mathrm{W}}_1$ < ${\mathrm{W}}_2$

3. ${\mathrm{W}}_1$ > ${\mathrm{W}}_2$

4. ${\mathrm{W}}_1$ = - ${\mathrm{W}}_2$

The variation of molar heat capacity at constant volume ${\mathrm{C}}_{\mathrm{V}}$ with temperature T for a monatomic gas is:

1.		2.
3.		4.

When a system is moved from state a to state b along the path acb, it is discovered that the system absorbs 200 J of heat and performs 80 J of work.  Along the path adb, heat absorbed Q = 144 J. The work done along the path adb is:

Heat is supplied to a diatomic gas in an isochoric process. The ratio $∆\mathrm{Q}:\hspace{0.17em}∆\mathrm{U}$ is: (symbols have usual meanings)

1. 5 : 3

2. 5: 2

3. 1: 1

4. 5: 7

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

The work done by an ideal diatomic gas in its sudden expansion is 20 J. The change in the internal energy of the gas will be:

1. 20 J

2. 0 J

3. $-20$ J

4. $-15$ J

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

If an ideal gas undergoes two processes at constant volumes ${\mathrm{V}}_1$ $\mathrm{and}$ ${\mathrm{V}}_2$ as shown in the pressure-temperature (P-T) diagram, then:

1. ${\mathrm{V}}_1$ = ${\mathrm{V}}_2$

2. ${\mathrm{V}}_1$ > ${\mathrm{V}}_2$

3. ${\mathrm{V}}_1$ < ${\mathrm{V}}_2$

4. ${\mathrm{V}}_1\ge {\mathrm{V}}_2$

The internal energy of an ideal gas increases in:

1. Adiabatic expansion

2. Adiabatic compression

3. Isothermal expansion

4. Isothermal compression

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

1. 129.6 J

2. $-$129.6 J

3. 149.6 J

4. $-$149.6 J