$A$ gas is compressed from a volume of $2 \,m^3$ to a volume of $1 \,m^3$ at a constant pressure of $100 \,N m^{-2}$. Then it is heated at constant volume by supplying $150 \,J$ of energy. As a result,the internal energy of the gas

Two moles of helium gas $\left(\gamma = \frac{5}{3}\right)$ at $27^{\circ} C$ is expanded at constant pressure until its volume is doubled. Then it undergoes an adiabatic change until the temperature returns to its initial value. The work done during the adiabatic process is (universal gas constant $R = 8.3 \ J \ mol^{-1} \ K^{-1}$) (in $J$)

The ratio of the work done, change in internal energy, and heat absorbed when a diatomic gas expands at constant pressure is

Check whether the following statements are true or false:
$1.$ The change in internal energy $\Delta U = 0$ in a cyclic process.
$2.$ In an adiabatic process,temperature remains constant.
$3.$ The internal energy of a system during an isothermal process decreases.

In Column-$I$ devices and in Column-$II$ efficiency are given. Match them appropriately:

Column-$I$	Column-$II$
$(a)$ Heat engine	$(i)$ $\eta = \frac{Q_2}{Q_1 - Q_2}$
$(b)$ Heat pump	$(ii)$ $\eta = \frac{Q_1 - Q_2}{Q_1}$
	$(iii)$ $\eta = \frac{T_1 - T_2}{T_1}$

Two cylinders $A$ and $B$ fitted with pistons contain an equal amount of an ideal diatomic gas at temperature $T$ $K$. The piston of cylinder $A$ is free to move,while that of $B$ is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise in temperature of the gas in $A$ is $dT_{A}$,then the rise in temperature of the gas in cylinder $B$ is (where $\gamma = \frac{C_{P}}{C_{V}}$):