Two identical samples of a gas are allowed to expand $(i)$ isothermally and $(ii)$ adiabatically. The work done is:

An ideal gas with constant heat capacity $C_V = \frac{3}{2} n R$ is made to carry out a cycle that is depicted by a triangle in the figure given below. The following statement is true about the cycle.

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

Which of the following processes will release the maximum amount of heat to the surroundings when the volume is reduced to half of its initial value?

$A$ polyatomic gas at pressure $P$,having volume $V$ expands isothermally to a volume $3V$ and then adiabatically to a volume $24V$. The final pressure of the gas is (for a polyatomic gas,assume degrees of freedom $f = 6$,so $\gamma = 4/3$):

$A$ given amount of gas has an initial state $(P_i, V_i, T_i)$. It expands until its volume becomes $V_f$. Consider the following two cases:
$(a)$ The expansion occurs at constant temperature (isothermal).
$(b)$ The expansion occurs at constant pressure (isobaric).
Draw the $P-V$ diagram for each case. In which of the two cases is the work done by the gas greater?