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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

Verified by Experts

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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Molar heat capacity of an ideal gas in the process PV^(x) = constant , is given by : C = (R)/(gamma-1) + (R)/(1-x) . An ideal diatomic gas with C_(V) = (5R)/(2) occupies a volume V_(1) at a pressure P_(1) . The gas undergoes a process in which the pressure is proportional to the volume. At the end of the process the rms speed of the gas molecules has doubled from its initial value. The molar heat capacity of the gas in the given process is :-

Knowledge Check

  • An ideal diatomic gas with C_(V)=(5R)/(2) occupies a volume V_(1) at a pressure P_(1) . The gas undergoes a process in which the pressure is proportional to the volume. At the end of the process the rms speed of the gas molecules has doubled from its initial value. Heat supplied to the gas in the given process is

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    `7p_(1)V_(1)`
    B
    `8p_(1)V_(1)`
    C
    `9p_(1)V_(1)`
    D
    `10p_(1)V_(1)`

  • An ideal diatomic gas with C_(V)=(5R)/(2) occupies a volume V_(1) at a pressure P_(1) . The gas undergoes a process in which the pressure is proportional to the volume. At the end of the process the rms speed of the gas molecules has doubled from its initial value. The molar heat capacity of the gas in the given process is

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    B
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    `9P_(1)V_(1)`
    D
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