An insulated box containing a diatomic gas of molar mass $M$ is moving with a velocity $v$. The box is suddenly stopped. The resulting change in temperature is (Where, $R$ is the gas constant)

$1$ mole of gas with $\gamma =\frac{7}{5}$ is mixed with $1$ mole of gas with $\gamma =\frac{5}{3}$, then the value of $\gamma$ for the resulting mixture is

An ideal gas is taken through the cycle $A\to B\to C\to A$, as shown in the figure below. If the net heat supplied to the gas is $5\mathrm{J}$, then the work done by the gas in the process $C\to A$ is