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

Options

A. `(2P_(0))/(3R) (P_(0)/(3a))^(1//2)`
B. `(3P_(0))/(2R) (P_(0)/(3a))^(1//2)`
C. `(P_(0))/(R) (P_(0)/(3a))^(1//2)`
D. `(P_(0))/(3R) (P_(0)/(3a))^(1//2)`

Answer

A

Explanation

` P= P_(0) -aV^(2)`
From ideal gas equation `PV = nRT`
`implies Rt = (P_(0)- aV^(2))V(n=1`)
`implies T = ((P_(0)V - aV^(3))/(R)) implies (dT)/(dV) = 0 = ((P_(0) - 3aV^(2))/(R))`
`implies V= sqrt((P_(0))/(3a))` and `(d^(2)T)/(dV^(2)) = -(6aV)/(R) (lt0)`.
`therefore T_(max) = ((P_(0)-aV^(2))V)/(R) = (2P_(0))/(3R)sqrt((P_(0))/(3a))`