For an ideal gas,the internal energy is given by $U = 5pV/2 + C$,where $C$ is a constant. The equation of the adiabats in the $pV$-plane will be

One mole of a monatomic ideal gas undergoes an adiabatic expansion in which its volume becomes eight times its initial value. If the initial temperature of the gas is $100 K$ and the universal gas constant $R = 8.0 J mol^{-1} K^{-1}$,the decrease in its internal energy,in Joule,is. . . . .

$A$ gas is kept in a container having walls which are thermally non-conducting. Initially,the gas has a volume of $800 \ cm^3$ and a temperature of $27^{\circ} C$. The change in temperature when the gas is adiabatically compressed to $200 \ cm^3$ is ......... $K$. (Take $\gamma=1.5$,where $\gamma$ is the ratio of specific heats at constant pressure and at constant volume.)

$A$ sample of gas at temperature $T$ is adiabatically expanded to double its volume. The work done by the gas in the process is (given $\frac{C_{P}}{C_{V}}=\gamma=\frac{3}{2}$,$R=$ gas constant).

In an adiabatic change,the pressure $P$ and temperature $T$ of a monoatomic gas are related by the relation $P \propto T^C$,where $C$ equals

In the following $P-V$ diagram, two adiabatics cut two isothermals at temperatures $T_1$ and $T_2$. The value of $\frac{V_a}{V_d}$ will be