Q. A sample of gas follows process represented by $P V^{2}=$ constant. Bulk modulus for this process is $B$, then which of the following graph is correct?

Thermodynamics Report Error

A

Option 1 Image

B

Option 2 Image

C

Option 3 Image

D

Option 4 Image

Solution:

$P V^{2}=$ constant
$\Rightarrow P \propto V^{-2}$
$\Rightarrow \frac{\Delta P}{P}=-2 \frac{\Delta V}{V}$
$\Rightarrow$ Bulk modulus
$K=\frac{\Delta P}{-\frac{\Delta V}{V}}=2 P$
As $P V=n R T$
So $K \propto \frac{1}{V^{2}}$ and $K \propto T^{2}$.

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