Question

The pressure, P, of a gas, varies inversely with its volume, V. Pressure is measured in units of Pa. Suppose that a particular amount of a gas is initially at a pressure of 84 Pa at a volume of 36 L. If the volume is expanded to 216 L, what will the new pressure be?

A. 6 Pa
B. 14 Pa
C. 216 Pa
D. 504 Pa
The answer is "B. 14 Pa"!

Answer 1

The pressure, P, of a gas, varies inversely with its volume, V

∴ PV = k where k is constant

The pressure is 84 Pa at a volume of 36 L.

∴ at P = 84 ⇒⇒⇒ V = 36

∴ K = PV = 84 * 36 = 3,024 ⇒⇒(1)

If the volume is expanded to 216 L, what will the new pressure be?
We need to find P at V = 216
From the equation (1) ⇒⇒⇒ PV = 3024
substitute with V = 216
∴ 216 P = 3024
∴ P = 3024/216 = 14

The correct answer is option B. 14 Pa