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0.014 kg N2 gas at 27^@C is kept in a cl...

0.014 kg `N_2` gas at `27^@C` is kept in a closed vessel. How much heat is required to double the rms speed of the `N_2` molecules?

Text Solution

Verified by Experts

Heat received, `Delta Q=nC_v Delta T`
[`C_v`=molar specific heat at constant volume]
Here, `n=(0.014 times 1000)/28=1/2`
For diatomic molecule, `C_v=5/2 R`
and rms speed of `N_2` molecule `c prop sqrt T`
`therefore` To double the velocity c, temperature should be 4T,
`thereforeDeltaQ=1/2times5/2Rtimes(4T-T)`
`=5/4times2times(273+27)times3[becauseR=2cal.mol^-1.K^-1`]
=2250 cal
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