The pressure of an ideal gas varies according to the law `P = P_(0) - AV^(2)`, where `P_(0)` and `A` are positive constants. Find the highest temperature that can be attained by the gas

Explanation

`P = P_(0) - AV^(2)`
`(n RT)/(V) = P_(0) - AV^(2)`
`T = (P_(0) V)/(n R) - (A V^(3))/(n R)`
For `T` to be maximum
`(d T)/(d V) = (P_(0))/(n R) - (A.3V^(2))/(n R) = 0`
`V = ((P_(0))/(3A))^(1//2)`
`T_(max) = (P_(0))/(n R)((P_(0))/(3 A))^((1)/(2)) - (A)/(n R)(P_(0))/(3 A)((P_(0))/(3A))^((1)/(2))`
`= (2)/(3)(P_(0))/(nR) sqrt((P_(0))/(3 A))`