Question

One mole of a diatomic gas (rigid molecule) does a work `|Q/2|` when the amount of heat supplied is ‘Q’. In this process the molar heat capacity of the gas is ______.

Options

• R

• 2 R

• 5 R

• 7 R

Answer 1

One mole of a diatomic gas (rigid molecule) does a work `|Q/2|` when the amount of heat supplied is ‘Q’. In this process the molar heat capacity of the gas is 5 R.

Explanation:

Given: W = `Q/2`

First law of thermodynamics:

Q = ΔU + W

∴ `Q = ΔU + Q/2`

∴ `ΔU = Q/2`   ...(i)

For a diatomic gas:

`ΔU = 5/2 R ΔT`   ...(ii)

Q = C_vΔT    ...(iii)

From (i), (ii), and (iii)

∴ `5/2 R ΔT = (C_v ΔT)/2`

∴ C_v = 5 R