Question

Equation of boyle`s law in term of differentiation

Answer 1

"Boyle's Law states that if the temperature of a gas remains constant, its pressure is inversely proportional to its volume. Use the derivative to show that the rate of change of the pressure is inversely proportional to the square of the volume."

Answer 2

SoluTion:

We know that,

P ∝ 1/V

→ P = k/V

→ PV = k

Differentiating on both sides,

P.dv + V.dp = 0

→ P.dv = -V.dp

→ dv/dp = -V/P ....(1)

Also, P = k/V....(2)

Put value of (2) in (1),

→ dv/dp = -V/(k/V)

→ dv/dp = -V²/k

→ (dv/dp)_T = -V²/k (i.e at constant temperature)

Hence, required formula is -V²/k.