An ideal gas having pressure $P$, volume $V$ and temperature $T$ is expanded isothermally to a volume $3V$ and final pressure $P_I$. The same gas is expanded adiabatically to a volume $3V$, the final pressure being $P_A$. The ratio $P_A/P_I$ is $(C_P/C_V = \gamma)$.

The coefficient of isothermal elasticity $E_{\theta}$ and the coefficient of adiabatic elasticity $E_{\phi}$ are related by $(\gamma = C_p/C_v)$.

In changing the state of a gas adiabatically from an equilibrium state $A$ to another equilibrium state $B$,an amount of work equal to $22.3 \; J$ is done on the system. If the gas is taken from state $A$ to $B$ via a process in which the net heat absorbed by the system is $9.35 \; cal$,how much is the net work done (in $J$) by the system in the latter case? (Take $1 \; cal = 4.19 \; J$)

The volume $V$ of a given mass of monoatomic gas changes with temperature $T$ according to the relation $V = KT^{2/3}$. The work done when temperature changes by $90\,K$ will be $xR$. The value of $x$ is $[R = \text{universal gas constant}]$

The ratio of the work done, change in internal energy, and heat absorbed when a diatomic gas expands at constant pressure is

$A$ gas may expand either adiabatically or isothermally. $A$ number of $P-V$ curves are drawn for the two processes over different ranges of pressure and volume. It will be found that: