Fill in the blank :

$1.$ The change of internal energy in cyclic process is ……

$2.$ The internal energy of gas is increased by ……

$3.$ An ideal gas at temperature $T_1$ is compressed to $32^{th}$ of its original volume, then its temperature $T_2$ will be …… $(\gamma = 1.4)$

$4.$ The triple point of water is at …… pressure and …… temperature.

The above $P-V$ diagram represents the thermodynamic cycle of an engine, operating with an ideal monatomic gas. The amount of heat, extracted from the source in a single cycle is

If a gas is taken from $A$ to $C$ through $B$ then heat absorbed by the gas is $8 \,J$. Heat absorbed by the gas in taking it from $A$ to $C$ directly is …………. $J$

When an ideal diatomic gas is heated at constant pressure, the fraction of the heat energy supplied which increases the internal energy of the gas, is

Two moles of monoatomic gas is expanded from $(P_0, V_0)$ to $(P_0 , 2V_0)$ under isobaric condition. Let $\Delta Q_1$, be the heat given to the gas, $\Delta W_1$ the work done by the gas and $\Delta U_1$ the change in internal energy. Now the monoatomic gas is replaced by a diatomic gas. Other conditions remaining the same. The corresponding values in this case are $\Delta Q_2 , \Delta W_2 , \Delta U_2$ respectively, then