Find the minimum attainable pressure of ideal gas in the process `T = T_0 + alpha V^2`, where `T_0` and `alpha` positive constants, and `V` is the volume of one mole of gas. Draw the approximate `p vs V` plot of this process.

Explanation

`T = T_0 + alpha V^2 = T_0 + alpha (R^2 T^2)/(p^2)`
(as, `V = RT//p-` for one mole of gas)
So, `p = sqrt(alpha) RT (T - T_0)^(1//2)` ….(1)
For `P_(min), (dp)/(dT) = 0`, which gives
`T = 2 T_0` …(2)
From (1) and (2), we get,
`p_(min) = sqrt(alpha) R 2 T_0 (2 T_0 - T_0)^(-1//2) = 2 R sqrt(alpha T_0)`.