Heat energy of $735\,J$ is given to a diatomic gas allowing the gas to expand at constant pressure. Each gas molecule rotates around an internal axis but does not oscillate. The increase in the internal energy of the gas will be $..........\,J$

Check if the following statements are true or false:
$1.$ For an adiabatic process,$T V^{\gamma - 1} = \text{constant}$.
$2.$ The charging process of a battery is a reversible process.
$3.$ Water falling from a height is a reversible process.
$4.$ Internal energy,volume,and mass are intensive variables,while pressure,temperature,and density are extensive variables.

If a heat engine and a refrigerator are working between the same two temperatures $T_1$ and $T_2$ $(T_1 > T_2)$,then the ratio of the efficiency of the heat engine to the coefficient of performance of the refrigerator is:

Two cylinders $A$ and $B$ are fitted with pistons and contain equal amounts of a diatomic gas at $300 \ K$. The piston of cylinder $A$ is free to move,while the piston of cylinder $B$ is fixed. If the same amount of heat is supplied to each cylinder,the temperature of gas in $A$ increases by $30 \ K$. What is the increase in the temperature of gas in $B$ (in $K$)?

Starting with the same initial conditions,an ideal gas expands from volume $V_{i}$ to $V_{f}$ in three different ways. The work done by the gas is $W_{1}$ if the process is purely isothermal,$W_{2}$ if the process is purely adiabatic,and $W_{3}$ if the process is purely isobaric. Then,choose the correct option.

Consider two containers $A$ and $B$ containing monoatomic gases at the same Pressure $(P)$,Volume $(V)$ and Temperature $(T)$. The gas in $A$ is compressed isothermally to $\frac{1}{8}$ of its original volume while the gas $B$ is compressed adiabatically to $\frac{1}{8}$ of its original volume. The ratio of final pressure of gas in $B$ to that of gas in $A$ is ...........