In an adiabatic change, the pressure p and temperature T of a diatomic gas are related by the relation `ppropT^alpha`, where `alpha` equals

Options

A. 2.5
B. 3.5
C. 1.4
D. 2.25

Answer

B

Explanation

For an adiabatic change `PV^(gamma)` = constant
But `V=(RT)/P" "thereforeP((RT)/P)^(gamma)="constant"`
`thereforeT^(gamma)P^(1-gamma)="Constant"`
`thereforePpropT^(gamma/(gamma-1))`
`therefore` Comparing with `PpropC^(2)`, we get `C=gamma/(gamma-1)`
For a diatomic gas, `gamma=7/5`
`thereforeC=(7/5)/(7/5-1)=7/2=3.5`