When a gas expands adiabatically,

The work done in which of the following processes is equal to the internal energy of the system?

If the given graph shows the logarithmic values of pressure $(P)$ and volume $(V)$ of an ideal gas, then the ratio of the specific heat capacities of the gas is

When $1 \text{ mole}$ of an ideal gas $(\gamma = 1.4)$ is compressed adiabatically,its temperature increases from $27^{\circ}C$ to $35^{\circ}C$. The increase in the internal energy of the gas is ...... $J$? $(R = 8.3 \text{ J/mol K})$

An engine takes in $5$ moles of air at $20\,^{\circ}C$ and $1\,atm$,and compresses it adiabatically to $1/10^{\text{th}}$ of the original volume. Assuming air to be a diatomic ideal gas made up of rigid molecules,the change in its internal energy during this process is $X\,kJ$. The value of $X$ to the nearest integer is

$5$ 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 $\left(R=8.30 \ J \ mol^{-1} \ K^{-1}\right)$.