Question

A diatomic gas undergoes adiabatic change. Its pressure 'P' and temperature 'T' are related as p ∝ T^x, where x is ______.

Options

• 3.0

• 1.5

• 2.5

• 3.5

Answer 1

A diatomic gas undergoes adiabatic change. Its pressure p and temperature T are related as p ∝ T^x, where x is 3.5.

Explanation:

For adiabatic change the relation between p and Tis given by

`"T"^gamma/("p"^(gamma - 1))` = constant

`"T"^gamma = "constant" xx "p"^(gamma - 1)`

`=> "T"^(gamma/(gamma - 1))` = constant × p

`=> "p" prop "T"^((gamma/(gamma - 1)))`

On comparing with given relation,

p ∝ T^x

x = `(gamma/(gamma - 1))`

For diatomic gas, `gamma = 7/5`

x = `((7//5)/(7//5 - 1))`

x = 3.5