Gas Heating at Constant Volume – Identify the Governing Law When a fixed mass of gas is heated in a rigid container (volume held constant), the pressure varies directly with absolute temperature according to Gay-Lussac's law (also called Amontons' law).

Introduction / Context:
Classical gas laws describe limiting cases of the ideal-gas equation. For safety and design of rigid vessels, we need the law that links pressure and temperature at constant volume.

Given Data / Assumptions:

• Fixed mass of gas.
• Constant volume (rigid container).
• Ideal-gas behavior near the operating state.

Concept / Approach:

The ideal-gas equation pV = m R T reduces to p ∝ T when V and m are constant. This direct proportionality is historically named Gay-Lussac's (or Amontons') law, whereas Boyle's law applies at constant temperature (p ∝ 1/V) and Charles' law at constant pressure (V ∝ T).

Step-by-Step Solution:

Verification / Alternative check:

Manometer or transducer readings in a heated rigid tank follow p ∝ T_K, confirming this law for gases near ideal behavior.

Why Other Options Are Wrong:

Boyle: constant temperature case; Charles: constant pressure case; Avogadro: equal volumes have equal moles at same p and T; Dalton: total pressure is sum of partial pressures in mixtures.

Common Pitfalls:

Using Celsius instead of Kelvin; mislabeling Charles and Gay-Lussac; assuming non-ideal effects negate the linear trend over small ranges (they typically do not).

Final Answer:

Gay-Lussac law