A one mole of an an ideal gas expands adiabatically at constant pressure such that its temperature `T prop (1)/(sqrt(V))`.

Options

A. 1.3
B. 1.5
C. 1.4
D. `2.0`

Answer

B

Explanation

In a adiabatic expansion, `PV^(gamma)` = constant
But `P = (RT)/(V) :. ((RT)/(V))V^(gamma)` = constant
`TV^(gamma - 1)` = constant or `T prop V^(1- gamma)`
As `T prop (1)/(sqrt(V)) :. 1 - gamma = - (1)/(2)`
or `gamma = 1 + (1)/(2) = (3)/(2) = 1.5`