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Question

# A gas consisting of rigid diatomic molecules is expanded adiabatically. How many times has the gas to be expanded to reduce the r.m.s. velocity of the molecules to (23) rd of initial value.

A
0.13
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B
7.6
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C
5
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D
3.8
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Solution

## The correct option is A 0.13Let vrmsis the root mean square velocity of a diatomic gas having γ=1.4 vrms=√3RTM vrms=√T To reduce rms velocity 2/3 times, temperature must reduce 4/9 times. i.e. T2=94T1 for an adiabatic process, T2Vγ−12=T1Vγ−11 (V2V1)γ−1=T1T2=49 V2V1=(49)1γ−1=(49)11.4−1=(49)2.5 V2V1=0.13 V2=0.13V1 Hence, gas will expand 0.13 times.

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