Question

At a constant temperature, the volume of a gas V is inversely proportional to it's pressure P.

By what percentage will the pressure of a gas change if it's volume increases by 25%?

Answer 1

Decrease by 20%

Explanation:

V = k/P

k = VP

25% increase is 125% of V

125/100 × V = 1.25V

k = 1.25V × pressure

VP = 1.25V × pressure

pressure = P/1.25

pressure = 0.8P

0.8P = 80% of P

Which is a 100 - 80 = 20% decrease

Answer 2

20% decrease

Explanation:

Volume is inversely proportional to pressure, so:

V = k/P

If we increase the volume by 25%:

1.25 V = k/P

P = k/(1.25 V)

P = 0.8 k/V

The initial pressure is P = k/V, so the final pressure is 80% of that. In other words, it decreases by 20%.