The maximum attainable temperature of an ideal gas in the process P=Po−αV2  (Where Po and α are positive constants,  n is a number of moles and R is universal gas constant) is

Given  P=Po−αV2Where Po  and α  are positive constantsFrom the ideal gas equationPV=nRT ∴Po−αV2V=nRT ⇒T=PoV−αV3nR If T is max then dTdV=00=1nRPo−3αV2 ⇒V=Po3α1/2 Corresponding pressure  P=Po−α.Po3α=2Po3⇒T=PVnR=2Po3RnPo3α1/2