Question

Pressure for polytropic process P varies with volume V as P=av-3, find out the bulk modulus.

• A. 3V
• B. 3P
• C. P
• D. V

Answer 1

Answer: (B)

3P

Answer 2

The bulk modulus (K) is defined as the ratio of the increase in pressure (ΔP) to the resulting decrease in volume (ΔV), when a material is subjected to an external pressure. Mathematically, it is expressed as:
$K = -V(\frac{ΔP}{ΔV})$
For a polytropic process where $P = av^-3$, we can write:
$\frac{dP}{dV} = (-3av^-4) = (\frac{-3P}{V})$Using the above relation, we can rewrite the bulk modulus as:
$K = -V(\frac{ΔP}{ΔV}) = -V(\frac{dP}{dV}) = -V(\frac{-3P}{V}) = 3P$
Therefore, the bulk modulus is 3 times the pressure, i.e., K = 3P.
Answer. B