A one mole of an ideal gas expands adiabatically at a constant pressure such that its temperature `Tpropto (1)/(sqrt(V))` .The value of the adiabatic constant gas is

Options

A. 1.3
B. 1.5
C. 1.67
D. 2

Answer

B

Explanation

In an adiabatic expansions
`PV^(gamma)=`constant
`P=(RT)/(V)`
`((RT)/(V))V^(gamma)=`constant
`TV^(gamma-1)=`constant or `T prop V_(1-gamma)`
As `T prop (1)/(sqrt(V)) therefore 1-gamma-(1)/(2)`
`gamma=1+(1)/(2)=(3)/(2)=1.5`