Gas laws — identifying Charles’ law: Select the statement that correctly represents Charles’ law for a fixed mass of gas.

Introduction / Context:
Classical gas laws provide limiting relationships of the ideal-gas equation when one property is held fixed. Recognizing which statement corresponds to Charles’ law is vital for quick problem setup in thermodynamics and fluid mechanics.

Given Data / Assumptions:

• Ideal-gas behavior with fixed mass.
• One property (pressure, volume, or temperature) held constant as specified.
• Absolute (Kelvin) temperature scale is used.

Concept / Approach:
Charles’ law states that at constant pressure, the volume of a fixed mass of gas is directly proportional to its absolute temperature. Mathematically, v ∝ T at constant p, or v/T = constant. Boyle’s law applies to p and v at constant T (p * v = constant), while Gay–Lussac’s law applies to p and T at constant v (p/T = constant).

Step-by-Step Solution:
From p * v = m * R * T, hold p constant.Then v is proportional to T ⇒ v/T = constant.Hence the correct statement is option B.

Verification / Alternative check:
Linear v–T plots at constant p extrapolate to zero volume at T = 0 K, consistent with the absolute scale.

Why Other Options Are Wrong:
Option A is Boyle’s law (constant temperature). Option C is Gay–Lussac’s law. Option D is a reciprocal form that is not the conventional statement at constant v.

Common Pitfalls:
Using Celsius instead of Kelvin in proportional relationships; confusing which property is held constant.

Final Answer:
v / T = constant, if p is kept constant