One mole of helium is adiabatically expanded from its initial state $({P_i},{V_i},{T_i})$ to its final state $({P_f},{V_f},{T_f})$. The decrease in the internal energy associated with this expansion is equal to

A tyre filled with air $({27^o}C,$ and $2$ atm) bursts, then what is temperature of air ……. $^oC$ $(\gamma = 1.5)$

One mole of an ideal gas expands adiabatically from an initial state $\left(T_A, V_0\right)$ to final state $\left(T_f, 5 V_0\right)$. Another mole of the same gas expands isothermally from a different initial state ( $T_{\mathrm{B}}, \mathrm{V}_0$ ) to the same final state $\left(T_{\mathrm{f}}, 5 V_0\right)$. The ratio of the specific heats at constant pressure and constant volume of this ideal gas is $\gamma$. What is the ratio $T_{\mathrm{A}} / T_{\mathrm{B}}$ ?

A diatomic gas initially at $18^o C$ is compressed adiabatically to one-eighth of its original volume. The temperature after compression will be

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 ………