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One kg of a diatomic gas is at a ...

One kg of a diatomic gas is at a pressure of `8 xx 10^(4) Nm^(-2)` the density of the gas if `4kg// m^(g)` .What is the energy of the gas due to its thermal mole

A

`3xx10^(4)J`

B

`5xx10^(4)J`

C

`6xx10^(4)J`

D

`7xx10^(4)J`

Text Solution

Verified by Experts

The correct Answer is:
B
Here, `m=1kg,rho=4kgm^(-3),P=8xx10^(4)Nm^(-2)`
`therefore V=(m)/(rho)=(1kg)/(4kgm^(-3))=(1)/(4)m^(3)`
As diatomic gas has 5 degrees of freedom, so the energy of the gas due to its thermal motion (or internal energy) is
`U=(5)/(2)nRT`, But `PV=nRT`
`therefore U=(5)/(2)PV=(5)/(2)xx8xx10^(4)xx(1)/(4)=5xx10^(4)J`
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