# Boyle's Law, Derivatives, and Rates of Change

• Sep 29th 2009, 12:47 PM
seuzy13
Boyle's Law, Derivatives, and Rates of Change
"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."

It's Greek to me. Help clarify it for me, please?
• Sep 29th 2009, 12:48 PM
e^(i*pi)
Quote:

Originally Posted by seuzy13
"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."

It's Greek to me. Help clarify it for me, please?

$P = \frac{k}{V}$ where k is constant.

You could take a time derivative but I don't see how that'd help
• Sep 29th 2009, 12:54 PM
seuzy13
Quote:

Originally Posted by e^(i*pi)
$P = \frac{k}{V}$ where k is constant.

You could take a time derivative but I don't see how that'd help

Hmm... could it possibly be that:
$
p' = \frac{v(k') - v'(k)}{v^2}
$

Shows they are inversely proportional?