The molar heat capacity in a process of a diatomic gas,if it does a work of $\frac{Q}{4}$ when a heat of $Q$ is supplied to it,is

Six moles of an ideal gas perform a cycle shown in the figure. If the temperatures are $T_A = 600\, K,$ $T_B = 800\, K,$ $T_C = 2200\, K,$ and $T_D = 1200\, K,$ then the work done per cycle is approximately ...... $kJ$.

$10 \text{ mole}$ of oxygen is heated at constant volume from $30^{\circ} C$ to $40^{\circ} C$. The change in the internal energy of the gas is . . . . . . $\text{cal}$. (The molecular specific heat of oxygen at constant pressure, $C_p = 7 \text{ cal/mol}^{\circ} C$ and $R = 2 \text{ cal/mol}^{\circ} C$.)

In changing the state of a gas adiabatically from an equilibrium state $A$ to another equilibrium state $B$,an amount of work equal to $22.3 \; J$ is done on the system. If the gas is taken from state $A$ to $B$ via a process in which the net heat absorbed by the system is $9.35 \; cal$,how much is the net work done (in $J$) by the system in the latter case? (Take $1 \; cal = 4.19 \; J$)

Two gases $A$ and $B$ are filled at the same pressure in separate cylinders with movable pistons of radius $r_A$ and $r_B$,respectively. On supplying an equal amount of heat to both the systems reversibly under constant pressure,the pistons of gas $A$ and $B$ are displaced by $16 \ cm$ and $9 \ cm$,respectively. If the change in their internal energy is the same,then the ratio $\frac{r_A}{r_B}$ is equal to

If heat energy $\Delta Q$ is supplied to an ideal diatomic gas,the increase in internal energy is $\Delta U$ and the amount of work done by the gas is $\Delta W$. The ratio $\Delta W: \Delta U: \Delta Q$ is