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Q.

A certain amount of ideal gas having degrees of freedom 6 undergoes a process for which Uβ proportional to V, where U is internal energy and V is volume of gas. It is found that the ratio ΔUΔQ for the process is 2/3. What is the value of β+5

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answer is 6.5.

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Detailed Solution

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UβαV, TβαV, PβVβαV

PβVβ−1=constant

P(V)(β−1)β=constant

ΔUΔQ=nCVΔTnCΔT=23

C=32Cv

CV+R1−x=32CV

where  x=β−1β⇒⇒β=32

β+5=132=6.5

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