A sample of $1$ mole gas at temperature $\mathrm{T}$ is adiabatically expanded to double its volume. If adiabatic constant for the gas is $\gamma=\frac{3}{2}$, then the work done by the gas in the process is:

A thermodynamic cycle $xyzx$ is shown on a $V-T$ diagram.

The $P-V$ diagram that best describes this cycle is

(Diagrams are schematic and not to scale)

An ideal monoatomic gas expands to twice its volume. If the process is isothermal, the magnitude of work done by the gas is $W_i$. If the process is adiabatic, the magnitude of work done by the gas is $W_a$. Which of the following is true?

Following figure shows $P-T$ graph for four processes $A, B, C$ and $D$. Select the correct alternative.

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 ${T_1}/{T_2}$ is given by