The equation PxVyTz = Constant is Charles’ law if

Analyze the question: We need the values of x, y, z that make P^x V^y T^z = constant reduce to Charles' law.

Concept: Charles' law says that for a fixed mass of gas at constant pressure, volume is directly proportional to absolute temperature:

V ∝ T, or V/T = constant

Solution:

• Pressure is constant in Charles' law, so P must drop out of the expression. That means x = 0 (since P⁰ = 1).
• Then we need V^y T^z = constant to match V/T = constant, which is V¹ T⁻¹.
• So y = 1 and z = -1.

This gives V¹T⁻¹ = constant, i.e. V/T = constant. ✔

Checking the other options:

• B: V⁻¹T = constant means T/V = constant. This is the same relationship written inverted, so it is also mathematically equivalent to Charles' law (V/T = 1/constant). Since the constant can be anything, B is also technically valid.
• C: PV = constant is Boyle's law.
• D: PV/T = constant is the general gas law.
• E: PVT = constant is not a gas law.

Note on the key: Options A and B are actually mathematically equivalent, because if V/T = k then T/V = 1/k, which is also a constant. So go with A.

Exam tip: For these "which law" questions, write the law in the form V/T = k, PV = k, or P/T = k, then match the powers. The variable that is held constant gets power 0.