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

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$\frac{a}{b}$

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

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

$\frac{b}{a}$

answer is B.

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Detailed Solution

$U = a + b P V = a + b n R T$

$\frac{d U}{d T} = n C_{V} = 0 + b n R; C_{V} = b R$

$C_{V} = \frac{R}{γ - 1}; b R = \frac{R}{γ - 1}; γ - 1 = \frac{1}{b}; γ = \frac{1 + b}{b}$

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