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) + alpha V^(2)where T_(0) and alpha are positive constants.

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

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) + alpha V^(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) + ALPHA V^(2)) [ "as" T = T_(0) + alpha V^(2) ] ` Here pressure P will be minimum, when `(dP)/(dV) = 0 " or " (dP)/(dV) = (RT_(0))/(V^(2)) + alpha R = 0 " or" V = sqrt((T_(0))/(alpha))` Thus pressure of the gas is minimum, when its volume is `V = sqrt((T_(0))/(alpha))` and at this volume , its temperature is given as `T = T_(0) + alpha V^(2) = T_(0) + alpha ( sqrt((T_(0))/(alpha)) )^(2) = 2T_(0)` Thus minimum VALUE of pressure is `P_(min) = (RT)/(V) = (R(2T_(0)))/(sqrt(T_(0)//alpha)) = 2R sqrt(T_(0) alpha)`