Two gases have the same initial pressure,volume,and temperature. They expand to the same final volume,one adiabatically and the other isothermally.

One mole of an ideal diatomic gas expands from volume $V$ to $2V$ isothermally at a temperature $27^{\circ} C$ and does $W$ joule of work. If the gas undergoes the same magnitude of expansion adiabatically from $27^{\circ} C$ doing the same amount of work $W$, then its final temperature will be (close to) . . . . . . ${ }^{\circ} C$.

Two cylinders $A$ and $B$ fitted with pistons contain equal amount of an ideal diatomic gas at $303 \text{ K}$. The piston of cylinder $A$ is free to move and that of cylinder $B$ 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 cylinder $B$ is $63 \text{ K}$, then the rise in temperature of the gas in $A$ is: (in $\text{ K}$)

The specific heat of hydrogen gas at constant pressure is $C_P = 3.4 \times 10^3 \text{ cal/kg } ^oC$ and at constant volume is $C_V = 2.4 \times 10^3 \text{ cal/kg } ^oC$. If $1 \text{ kg}$ of hydrogen gas is heated from $10^oC$ to $20^oC$ at constant pressure,the external work done by the gas is:

An ideal gas is subjected to a cyclic process involving four thermodynamic states. The amounts of heat $(Q)$ and work $(W)$ involved in each of these states are:
$Q_1 = 6000 \ J, Q_2 = -5500 \ J, Q_3 = -3000 \ J, Q_4 = 3500 \ J$
$W_1 = 2500 \ J, W_2 = -1000 \ J, W_3 = -1200 \ J, W_4 = x \ J$
The ratio of the net work done by the gas to the total heat absorbed by the gas is $\eta$. The values of $x$ and $\eta$ respectively are:

Consider one mole of helium gas enclosed in a container at initial pressure $P_1$ and volume $V_1$. It expands isothermally to volume $4 V_1$. After this,the gas expands adiabatically and its volume becomes $32 V_1$. The work done by the gas during isothermal and adiabatic expansion processes are $W_{\text{iso}}$ and $W_{\text{adia}}$,respectively. If the ratio $\frac{W_{\text{iso}}}{W_{\text{adia}}} = f \ln 2$,then $f$ is: