The temperature and volume of one mole an ideal gas during its expansion is related as $T = T_{0} + α V^{2}$ where $T_{0}$ and $α$ positive constants. R is the universal gas constant.
The volume at which the pressure is minimum is;

Q. One mole of an ideal gas with heat capacity at constant pressure

C_{p}

undergoes the process

T = T_{0} + α V

where

T_{0}

and

α

are constants. If its volume increases from

V_{1}

V_{2}

, the amount of heat transfered to the gas is

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One mole of an ideal gas undergoes a process in which T=T0+aV3, where T0 and 'a' are positive constants and V is volume. The volume for which the pressure of the gas will be minimum is

The correct option is A (T02a)1/3For ideal gas PV=nRT, so LHS can be written as T=PVnR .Now find the relation of P wrt VPV=To+aV3→P=ToV+aV2,differentiating the eq wrt to V and putting the eq as The volume for which the pressure of the gas will be minimum is dPdV=0we get V=(To2a)1/3

One mole of an ideal gas undergoes a process in which $T = T_{0} + a V^{3}$ , where $T_{0}$ and 'a' are positive constants and V is volume. The volume for which the pressure of the gas will be minimum is