Heating a Gas at Constant Volume – What Changes? When a gas is heated in a rigid, constant-volume container, its temperature rises and, for an ideal gas, the pressure increases proportionally to the absolute temperature.

Introduction / Context:
Understanding which properties change during constrained heating is essential for safe vessel design and control. The classic case of a rigid tank emphasizes the role of the ideal gas law and constant-volume specific heat in predicting state changes.

Given Data / Assumptions:

• Rigid, sealed container (V = constant).
• Gas behaves ideally over the temperature range considered.
• No mass enters or leaves; neglect changes in kinetic and potential energy.

Concept / Approach:

Energy balance for a closed, rigid system gives Q = ΔU = m * Cv * (T2 − T1). Thus, adding heat raises temperature. The ideal gas law pV = mRT then implies p ∝ T when V and m are fixed, so pressure also increases proportionally to absolute temperature.

Step-by-Step Solution:

Verification / Alternative check:

Manometer readings in a heated rigid cylinder rise with temperature; tabulated compressibility factors near unity corroborate the proportionality for many gases at moderate pressures.

Why Other Options Are Wrong:

Temperature or pressure increasing alone contradicts the coupled relationship via pV = mRT. No change in either violates the first law for nonzero Q. A decrease in temperature upon heating is unphysical for a simple gas in a rigid container.

Common Pitfalls:

Confusing constant-volume with constant-pressure heating; forgetting that even small temperature rises can cause significant pressure increases in tightly sealed vessels.

Final Answer:

both temperature and pressure will increase