Question

# For a reversible adiabatic expansion of an ideal gas $$dp/p$$ equal to:

A
γdvv
B
dvv
C
(γγ1)dvv
D
γdvv

Solution

## The correct option is D $$-\gamma \dfrac{dv}{v}$$Solution:- (D) $$-\gamma \cfrac{dv}{v}$$In an adiabatic process,$$p{v}^{\gamma} = K \left( \text{constant} \right)$$Differentiating the above equation, we have$$\left( 1. dp \right) {v}^{\gamma} + p. \left( \gamma {v}^{\gamma - 1} dv \right) = 0$$$$dp {v}^{\gamma} = - \gamma p {v}^{\gamma - 1} dv$$$$\cfrac{dp}{p} = \cfrac{-\gamma {v}^{\gamma -1}}{{v}^{\gamma}} dv$$$$\cfrac{dp}{p} = -\gamma \cfrac{dv}{v}$$Here $$\cfrac{dp}{p}$$ and $$\cfrac{dv}{v}$$ are the fractional change in pressure and volume respectively.Chemistry

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