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The relation between internal energy U, pressure P and volume V of a gas in an adiabatic process is U = a+bPV, where a and b are positive constants. What is the value of $γ$ ?

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$\frac{a + 1}{a}$

$\frac{b + 1}{b}$

$\frac{b}{a}$

$\frac{a}{b}$

answer is B.

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Detailed Solution

as U = a+bPV

differentiating both the side

du = d(a) +d(bPV)

du = 0+bd(PV)

du = bnRdT

comparing with $d u = \frac{f}{2} n R d T$

$\frac{f}{2} = b$ and $γ = \frac{2 + f}{f}$

solving $γ = \frac{1 + b}{b}$

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