If $\gamma = 2.5$ and the final volume is $\frac{1}{8}$ times the initial volume, then the final pressure $P'$ is equal to (Initial pressure $= P$).

An ideal gas in a cylinder is compressed adiabatically to one-third of its original volume. $A$ work of $45 \,J$ is done on the gas by the process. The change in internal energy of the gas and the heat flowed into the gas, respectively are

$A$ van der Waals gas obeys the equation of state $\left(p+\frac{n^2 a}{V^2}\right)(V-n b)=n R T$. Its internal energy is given by $U=C T-\frac{n^2 a}{V}$. The equation of a quasistatic adiabat for this gas is given by

In an adiabatic expansion of a gas,

$A$ fixed amount of a gas undergoes a thermodynamic process as shown in the figure,such that the heat interaction along path $B \to C \to A$ is equal to the work done by the gas along path $A \to B \to C$. Then the process $A \to B$ is:

During an adiabatic process,the pressure of the gas is found to be proportional to the cube of its absolute temperature. The ratio $C_P/C_V = \gamma$ for the gas is: