find the minimum attainable pressure of an ideal gs in the process `T = t_0 + prop V^2`, where `T_(0)n` and `alpha` are positive constants and (V) is the volume of one mole of gas.
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Correct Answer – B
`p = (R T)/(V)` `(n = 1)`
or `p = (R) /(V) (T_0 + alpha V^2)`
For minimum attainable pressure
`(d p)/(d V) = 0 or (- R T_0)/(V^2) + alpha R = 0`
or `V = sqrt((T_0)/(alpha))`
At this volume we can see that `(d^2 p)/(d V^2)` is positive or (p) is minimum.
From Eq. (i)
`p_(min) = (R T_0)/(sqrt(T_0//alpha)) + alpha R sqrt(T _0 // prop)`
= `2 R sqrt (alpha T_0)`.