When an ideal diatomic gas is heated at constant pressure, the fraction of the heat energy supplied, which increases the internal energy of the gas, is

Options

A. `2/5`
B. `5/7`
C. `3/7`
D. `3/5`

Answer

B

Explanation

The heat supplied to the gas `dQ=nC_(P)dT`
and the increase in the internal energy `dU=nC_(V)dT`.
Where n is the number of moles and `C_(P) and C_(V)` are the specific heats of the gas at constant pressure and constant volume respectively.
The fraction of the total energy used for internal energy
`(dU)/(dQ)=(nC_(V)dT)/(nC_(P)dT)=C_(V)/C_(P)`
But `C_(V)/C_(P)=1/gamma`
and for a diatomic gas molecule, there are five degrees of freedom and `gamma=1+2/f=1+2/5=7/5`
`therefore` Fraction = `1/gamma=5/7`