An ideal gas in a thermally insulated vessel at internal pressure = ${\mathrm{P}}_1$ , volume = ${\mathrm{V}}_1$ and absolute temperature = ${\mathrm{T}}_1$ expands irreversibly against zero external pressure, as shown in the diagram. The final internal pressure, volume and absolute temperature of the gas are ${\mathrm{P}}_2$ , ${\mathrm{V}}_2$ and ${\mathrm{T}}_2$ , respectively. For this expansion,