Given the relation $V = K \left( \frac{P}{T} \right)^{0.33}$,where $K$ is a constant. Identify the type of thermodynamic process.

If $\gamma$ is the ratio of molar specific heat at constant pressure to molar specific heat at constant volume for a gas,find the change in internal energy of $1 \, mol$ of the gas when its volume changes from $V$ to $2V$ at constant pressure $P$.

Work done by $0.1$ mole of a gas at $27^{\circ}C$ to double its volume at constant pressure is ....... $cal$ $(R = 2 \, cal \, mol^{-1} \, K^{-1})$.

$A$ container having $1$ mole of a gas at a temperature $27^{\circ}C$ has a movable piston which maintains a constant pressure in the container of $1 \, atm$. The gas is compressed until the temperature becomes $127^{\circ}C$. The work done is ........ $J$ ($C_P$ for the gas is $7.03 \, cal/mol-K$).

At constant pressure,what fraction of the heat supplied to an ideal gas is converted into mechanical work?

$A$ gas expands under constant pressure $P$ from volume $V_1$ to $V_2$. The work done by the gas is