$A$ monoatomic gas $\left(\gamma=\frac{5}{3}\right)$ at a pressure of $4 \text{ atm}$ is compressed adiabatically so that its temperature rises from $27^{\circ} \text{C}$ to $327^{\circ} \text{C}$. The pressure of the gas in its final state is

$A$ sample of an ideal gas is contained in a cylinder. The volume of the gas is suddenly decreased. $A$ student makes the following statements to explain the change in pressure of the gas:
$I.$ The average kinetic energy of the gas atoms increases.
$II.$ The atoms of the gas hit the walls of the cylinder more frequently.
$III.$ Temperature of the gas remains unchanged.
Which of these statements is true?

$A$ bicycle tire tube is inflated using a pump. Assume the volume of the tube $V$ is constant and in each stroke,an amount of air $\Delta V$ is pushed into the tube under an adiabatic process. What is the work done to increase the pressure in the tube from $P_{1}$ to $P_{2}$?

$A$ monatomic gas at $630 \,K$ expands adiabatically to $27$ times its initial volume. The final temperature of the gas is (in $\,K$)

An ideal gas initially at $0^{\circ} C$ temperature, is compressed suddenly to one fourth of its volume. If the ratio of specific heat at constant pressure to that at constant volume is $3/2$, the change in temperature due to the thermodynamics process is . . . . . . $K.$

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.)