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Equipartition Theorem

The relation ...

Question

The relation between U,P and V for ideal gas is U=2+3PV. What is the adiabatic coefficient of gas

1.33

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1.4

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1.5

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1.67

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Solution

The correct option is D 1.67
$U = 2 + 3 P V$
$= 2 + 3 R T$ (Ideal gas:PV=RT)
$C_{V} = {(\frac{\partial U}{\partial T})}_{V} = 3 R$ (Specific heat at constant volume)
Also, $C_{P} - C_{V} = R$
$C_{P} = C_{V} + R = 4 R$ (Specif heat at constant pressure)
Adiabatic coefficient , $γ = \frac{C_{P}}{C_{V}} = \frac{4 R}{3 R} = \frac{4}{3} = 1.67$

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