Find the minimum attainable pressure of one mole of an ideal gas if during its expansion its temperature and volume are related as T=T_(0)+alphaV^(2) where T_(0)" and "alpha are positive constants.

Find the minimum attainable pressure of one mole of an ideal gas if du

1.	Find the minimum attainable pressure of one mole of an ideal gas if during its expansion its temperature and volume are related as T=T_(0)+alphaV^(2) where T_(0)" and "alpha are positive constants.
Answer» Solution :GIVEN that one mole of gas is used, thus from gas law, we have PV = RT or `P=(RT)/V=R/V(T_(0)+alphaV^(2))""["as "T=T_(0)+alphaV^(2)]` Here pressure P will be minimum when `(dP)/(DV)=0" or "(dP)/(dV)=(RT_(0))/V^(2)+alphaR=0" or "V=sqrt(T_(0)/alpha)` Thus pressure of gas is minimum when its volume is `V=sqrt(T_(0)/alpha)` and at this volume its temperature is given as `T=T_(0)+alphaV^(2)` `T=T_(0)+alpha(sqrt(T_(0)/alpha))^(2)=2T_(0)` Thus minimum value of pressue is `rArr P_(MIN)=(RT)/V=(R(2T_(0)))/sqrt(T_(0)//alpha)=2Rsqrt(T_(0)alpha)`