One mole of a diatomic gas does a work $\frac{Q}{3}$,when the amount of heat supplied is $Q$. In this process,the molar heat capacity of the gas is:

An ideal monoatomic gas with pressure $P$, volume $V$ and temperature $T$ is expanded isothermally to a volume $2V$ and a final pressure $P_i$. If the same gas is expanded adiabatically to a volume $2V$, the final pressure is $P_a$. The ratio $\frac{P_a}{P_i}$ 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:

$A$ bubble containing $8$ moles of Helium is submerged at a certain depth in water. When the temperature of the water increases by $30 \ ^\circ C$,how much heat in $J$ is added during the expansion of the Helium bubble?

Air in a cylinder is suddenly compressed by a piston,which is then maintained at the same position. With the passage of time,

Neon gas of a given mass expands isothermally to double its volume. What should be the further fractional decrease in pressure,so that the gas when adiabatically compressed from that state,reaches the original state?