If during an adiabatic process the pressure of mixture of gases is found to be proportional to square of its absolute temperature. The ratio of $C_p / C_v$ for mixture of gases is .........

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

In an adiabatic process where in pressure is increased by $\frac{2}{3}\% $ if $\frac{{{C_p}}}{{{C_v}}} = \frac{3}{2},$ then the volume decreases by about

Neon gas of a given mass expands isothermally to double volume. What should be the further fractional decrease in pressure, so that the gas when adiabatically compressed from that state, reaches the original state?

Consider one mole of helium gas enclosed in a container at initial pressure $P_1$ and volume $V_1$. It expands isothermally to volume $4 V_1$. After this, the gas expands adiabatically and its volume becomes $32 V_1$. The work done by the gas during isothermal and adiabatic expansion processes are $W_{\text {iso }}$ and $W_{\text {adia, }}$ respectively. If the ratio $\frac{W_{\text {iso }}}{W_{\text {adia }}}=f \ln 2$, then $f$ is. . . . . . . .

A sample of gas at temperature $\mathrm{T}$ is adiabatically expanded to double its volume. Adiabatic constant for the gas is $\gamma=3 / 2$. The work done by the gas in the process is : $(\mu=1 \mathrm{~mole})$