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An ideal diatomic gas with CV = (5 R)/2 ...

An ideal diatomic gas with `C_V = (5 R)/2` occupies a volume `(V_(i)` at a pressure `(P_(i)`. The gas undergoes a process in which the pressure is proportional to the volume. At the end of the process, it is found that the rms speed of the gas molecules has doubles from its initial value. Determine the amount of energy transferred to the gas by heat.

Text Solution

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The correct Answer is:
A, D
Given that, `p prop V or pV^-1 = constant`
As we know, moler heat capacity in the process `pV^x = constant is`
`C = R/(gamma - 1)+ R/(1 - x)= C_V + R/(1 - x)`
In the given problem,
`C_v = (5 R)/2 and x= -1`
`:. C = (5 R)/2 +R/2 = 3R` ...(i)
At the end of the process rms speed is doubled, (i.e). temperature has become four times `(v_(rms prop sqrt (T)))`.
Now, `Delta Q = n C Delta T`
= `n C(T_f - T_i)`
= `nC (4 T _i - T_i)`
=`3 T_i nC`
=`(3 T_i) (n) (3 R)`
= `9 (n RT_i)`
or `Delta Q = 9 P_i V_i`.
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