An ideal gas expands in such a way that $PV^2 =$ constant throughout the process.

$P_i, V_i$ and $P_f, V_f$ are initial and final pressures and volumes of a gas in a thermodynamic process respectively. If $PV^n = \text{constant}$, then the amount of work done is

An ideal gas is subjected to a thermodynamic process $PV^{2.5} = 0.40$,where $P$ is in $Pa$ and $V$ is in $m^3$. What is the slope of the $P-V$ curve with volume plotted against the $x-$axis at $V = 1 \, m^3$?

The $P-V$ diagram of a diatomic gas is a straight line passing through the origin. The molar heat capacity of the gas in this process will be:

Find the amount of work done to increase the temperature of one mole of an ideal gas by $30^o\ C$ if it is expanding under the condition $V \propto T^{2/3}$. $[R = 1.99 \ cal/mol-K]$

An ideal gas undergoes a quasi-static,reversible process in which its molar heat capacity $C$ remains constant. If during this process the relation of pressure $P$ and volume $V$ is given by $PV^n = \text{constant}$,then $n$ is given by (Here $C_p$ and $C_v$ are molar specific heat at constant pressure and constant volume,respectively):