One mole of an ideal gas $(\gamma = 1.4)$ is adiabatically compressed so that its temperature rises from $27\,^{\circ}C$ to $35\,^{\circ}C$. The change in the internal energy of the gas is .... $J$ (given $R = 8.3 \,J/mol/K$)

In a thermodynamic system,$W$ represents the work done by the system and $\Delta U$ is the increase in internal energy. Which of the following statements is $TRUE$?

In an adiabatic change,the pressure $P$ and temperature $T$ of a diatomic gas are related by the relation $P \propto T^C$,where $C$ is equal to:

$5$ moles of Hydrogen $\left(\gamma=\frac{7}{5}\right)$ initially at $S.T.P.$ are compressed adiabatically so that its temperature becomes $400^{\circ} C$. The increase in the internal energy of the gas in kilo-joules is $\left(R=8.30 \ J \ mol^{-1} \ K^{-1}\right)$.

$5.6\, L$ of helium gas at $STP$ is adiabatically compressed to $0.7\, L$. Taking the initial temperature to be $T_1$,the magnitude of work done in the process is

$A$ polyatomic gas is compressed to $\left(\frac{1}{8}\right)^{\text{th}}$ of its original volume adiabatically. If its initial pressure is $P_0$,what will be its new pressure (in $P_0$)? (Given: $\gamma = \frac{C_p}{C_v} = \frac{4}{3}$)