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

An ideal gas undergoes an adiabatic process obeying the relation $PV^{4/3} = \text{constant}$. If its initial temperature is $300 \ K$ and its pressure is increased up to four times its initial value, then the final temperature is (in Kelvin):

By what factor should the volume of an ideal gas $(\gamma = 1.5)$ be increased through an adiabatic expansion so that its $rms$ speed becomes half?

Which of the following is true in the case of an adiabatic process, where $\gamma = C_p / C_V$?

The equation of state of $n$ moles of a non-ideal gas can be approximated by the equation $\left(p+\frac{n^2 a}{V^2}\right)(V-n b)=n R T$,where $a$ and $b$ are constant characteristics of the gas. Which of the following can represent the equation of a quasistatic adiabat for this gas? (Assume that $C_V$,the molar heat capacity at constant volume,is independent of temperature.)

$A$ diatomic gas $\left(\gamma = \frac{7}{5}\right)$ is compressed adiabatically to volume $\frac{V_0}{32}$,where $V_0$ is its initial volume. The initial temperature of the gas is $T_i$ in Kelvin and the final temperature is $xT_i$ in Kelvin. The value of $x$ is: