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Question

An ideal gas having initial pressures P, volume V and temperature R is allowed to expand adiabatically until its volume becomes 5.66 V while its temperature falls to T/2. How many degrees of freedom do the gas molecules have?

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Solution

For an adiabatic change
(VV)(gamma1)=TT
Given V=5.66 V and T=T2.
(5.66)(γ1)=2
(γ1)log(5.66)=log(2)

γ=1+log(2)log(5.66)=1+0.30100.7528=1+0.4=1.4

Since γ=1.4, the gas is diatomic. For a diatomic gas, the number of degrees of freedom of the molecules =5.

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