A gas undergoes a process in which the pressure is $P$ , the volume is $V$ and they are related as $V P^{n} = c o n s t a n t$ . What is the bulk modulus of the gas in this process?

n P

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P^{1 / n}

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\frac{P}{n}

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P^{n}

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Solution

The correct option is C $\frac{P}{n}$
The equation for the thermodynamic process is given as $V P^{n} =$ constant
Differentiating with respect to V, we get
$P^{n} + V n P^{n - 1} \frac{d P}{d V} = 0$
$P + n V \frac{d P}{d V} = 0$
$\Rightarrow \frac{P}{n} = - V \cdot \frac{d P}{d V} = - \frac{d P}{(\frac{d V}{V})} =$ bulk modulus of gas

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