One kg of a diatomic gas is at a pressure of `8 xx 10^(4) N//m^(2)`. The density of the gas is `4kg//m^(3)`. What is the energy of the gas due to its thermal motion ?

Options

A. `3 xx10^4 J`
B. `5 xx10^4 J`
C. `6 xx10^4 J`
D. `7 xx10^4 J`

Answer

B

Explanation

Thermal energy corresponds to internal energy
Mass = 1 kg
Density `=4kgm^(-3)`
volume `=(" Mass ")/(" Density ")= (1)/(4)m^3`
Pressure `=8xx10^(4)Nm^(-2)`
As internal energy `=(f)/(2)nRT=(f)/(2)pv`
Degree of fredom for diatomic =5
internal energy `=(5)/(2)xxv`
Putting the values of `p=8xx 10^(4) Nm^(-2)" and "v=(1)/(4)m^2`, we get
internal energy `=(5)/(2)xx8xx10^(4)xx(1)/(4)=5xx10^(4)J`.