$A$ tyre filled with air ($27^\circ C$ and $2 \text{ atm}$) bursts. What is the final temperature of the air in $^\circ C$? (Given: $\gamma = 1.5$)

$A$ van der Waals gas obeys the equation of state $\left(p+\frac{n^2 a}{V^2}\right)(V-n b)=n R T$. Its internal energy is given by $U=C T-\frac{n^2 a}{V}$. The equation of a quasistatic adiabat for this gas is given by

An ideal monoatomic gas of volume $V$ is adiabatically expanded to a volume $3V$ at $27^{\circ}C$. The final temperature in Kelvins is (use $\frac{C_P}{C_V} = \frac{5}{3}$)

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

$A$ certain volume of a gas at $300 \ K$ expands adiabatically until its volume is doubled. The resultant fall in temperature of the gas is nearly (The ratio of the specific heats of the gas $\gamma = 1.5$) (in $K$)

$A$ diesel engine has a compression ratio of $20:1$. If the initial pressure is $1 \times 10^5 \ Pa$ and the initial volume of the cylinder is $1 \times 10^{-3} \ m^3$,then how much work does the gas do during the compression (in $J$)? (Assume the process as adiabatic) $(C_V=20.8 \ J/mol \ K, \gamma=1.4, (20)^{1.4}=66.3)$