n moles of an ideal gas undergo a thermodynamic process in which pressure of gas varies linearly with the volume of gas as shown in figure. If P0V0nR=200K, find the maximum temperature of the gas during the process (in K).

Gas pressure is given as Slope=2P0-P0V0-2V0=-P0V0   P−2P0=−P0V0V−V0⇒P=3P0−P0V0V     T=PVnR=3P0nRV−P0nRV0V2T is maximum when dTdV=0          dTdV=3P0nR−2P0nRV0V=0 or, V=3V02⇒ Tmax=3P0nR3V02−P0nRV032V02                   =92P0V0nR−94P0V0nR=9P0V04nR⇒      Tmax=94×200=450K