In thermodynamic processes, which of the following statements is not true?

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

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: $\gamma = 1.5$]

In the following figures, four curves A, B, C and D, are shown. The curves are:

A monoatomic ideal gas, initially at temperature $T_1$, is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature $T_2$ by releasing the piston suddenly. If $L_1$ and $L_2$ are the lengths of the gas column before and after expansion, respectively, then $\frac{T_1}{T_2}$ is given by:
1. $\left(\frac{L_1}{L_2}\right)^{\frac{2}{3}}$
2. $\frac{L_1}{L_2}$
3. $\frac{L_2}{L_1}$
4. $\left(\frac{L_2}{L_1}\right)^{\frac{2}{3}}$

The pressure and volume of a gas are changed as shown in the P-V diagram. The temperature of the gas will:

The figure shows the $(P\text-V)$ diagram of an ideal gas undergoing a change of state from $A$ to $B.$ Four different paths $\mathrm{I, II, III}$ and $\mathrm{IV},$ 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 $1, 2~\text{and}~3$, as shown in the figure. If $W_1, W_2~\text{and}~W_3$ respectively be the work done by the gas along the three paths, then: