Find the minimum attainabel pressure of one mole of an ideal gas. If during its expansion its temprature and volume are related as `T=T_(0)+alphaV^(2)` where `T_(0)&alpha` are positive constants

Options

A. `2Rsqrt(T_(0)alpha)`
B. `(Rsqrt(T_(0)alpha))/(2)`
C. `Rsqrt(T_(0)alpha)`
D. `(Rsqrt(T_(0)alpha))/(4)`

Answer

A

Explanation

`P = (RT)/(V) = (R)/(V) (T_(0) + alphaV^(2))`
`(dp)/(dV) = 0 rarr V = sqrt((T_(0))/(alpha))`
`T = T_(0) + alpha(sqrt((T_(0))/(alpha)))^(2) = 2T_(0)`
`P_(min) = (RT)/(V) = (R(2T_(0)))/(sqrt(T_(0)//alpha)) = 2Rsqrt(T_(0)alpha)`