The figure shows the (P-V) diagram of an ideal gas undergoing a change of state from A to B. Four different paths I, II, III and IV, as shown in the figure, may lead to the same change of state.
               

Which of the following options contains only correct statements?

Work done during the given cycle is:
                               
1. 4$P_0{V}_0$

2. 2$P_0{V}_0$

3. $\frac{1}{2}$$P_0{V}_0$

4. $P_0{V}_0$

A given mass of gas expands from state A to state B by three paths, 1, 2 and 3, as shown in the figure. If ${\mathrm{W}}_1,$ ${\mathrm{W}}_2$ $\mathrm{and}$ ${\mathrm{W}}_3$ respectively be the work done by the gas along the three paths, then:

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 pressure of a monoatomic gas increases linearly from $4\times {10}^5$ N/m² to $8\times {10}^5$ N/m² when its volume increases from 0.2 m³ to 0.5 m³. The work done by the gas is:

1. $2.8\times {10}^5 \mathrm{J}$

2. $1.8\times {10}^6 \mathrm{J}$

3. $1.8\times {10}^5 \mathrm{J}$

4. $1.8\times {10}^2 \mathrm{J}$

Two identical samples of a gas are allowed to expand, (i) isothermally and (ii) adiabatically. Work done will be:

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