Adiabatic reversible expansion of a gas is represented by

Options

A. `((T_(1))/(T_(2)))^(gamma)=((P_(2))/(P_(1)))^(1-gamma)`
B. `((T_(1))/(T_(2)))^(gamma)=((P_(1))/(P_(2)))^(1-gamma)`
C. `((T_(1))/(T_(2)))^(gamma)=((P_(1))/(P_(2)))^(gamma-1)`
D. All of the above

Answer

C

Explanation

`T_(1)V_(1)^((gamma-1))`
`T_(2)V_(2)^((gamma-1))`
or `(T_(1))/(T_(2))=((V_(2))/(V_(1)))^(gamma-1)`
According to ideal gas equation for 1 mole
`PV=RT`
`(V_(2))/(V_(1))=((T_(2))/(T_(1)))((P_(1))/(P_(2)))`
From equations `(1)` and `(2)` , we get
`(T_(1))/(T_(2))=((T_(2))/(T_(1)))^(gamma-1)((P_(1))/(P_(2)))^(gamma-1)`
`((T_(1))/(T_(2)))^(gamma)=((P_(2))/(P_(1)))^(1-gamma)`