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

Answer

1

Explanation

`P=P_(0)-alphaV^(2)`
`("nRT")/("V")=P_(0)-alphaV^(2)`
`RT=P_(0)V-alphaV^(3)" "[becausen=1]`
`(dT)/(dV)=(P_(0))/(R)-(3alphaV^(2))/(R)=0`
`V=sqrt((P_(0))/(3alpha))`
`RT=P_(0)sqrt((P_(0))/(3alpha))-alpha(P_(0))/(3alpha)sqrt((P_(0))/(3alpha))`
`T_("max")=(sqrtP_(0))/(sqrt3alphaR)(P_(0)-(P_(0))/(3))=(2P_(0))/(3R)sqrt((P_(0))/(3alpha))`