Questions: Boyle's and Charles' Laws for Ideal Gases

Question 1

A gas at 50°C is heated to 100°C at constant pressure. A student doubles the volume, reasoning that the temperature doubled. Is the student correct?

• A. Yes — the temperature doubled from 50 to 100, so volume doubles by Charles' Law
• B. No — Charles' Law only applies when pressure changes, not temperature
• C. No — the Kelvin temperatures are 323 K and 373 K, so volume increases by a factor of 373/323, not 2
• D. No — Boyle's Law applies here, not Charles' Law

Answer: (C)

The student made the classic Celsius mistake. Charles' Law requires absolute temperature (Kelvin). 50°C = 323 K and 100°C = 373 K. The temperature did NOT double — it increased by a factor of 373/323 ≈ 1.15. Only on the Kelvin scale does doubling temperature actually represent a doubling of molecular kinetic energy, making the proportionality V/T = constant valid. Using Celsius breaks the direct proportionality because 0°C is not the true zero of thermal energy.

Question 2

A gas is stored in a sealed, rigid container. The container is heated. What happens to the gas pressure, and which law applies?

• A. Pressure stays constant — Boyle's Law holds because volume is fixed
• B. Boyle's Law does not apply here — it requires constant temperature, and this scenario involves changing temperature
• C. Pressure doubles as temperature doubles, per Charles' Law
• D. Pressure decreases as the molecules slow down and spread out

Answer: (B)

Boyle's Law (PV = constant) holds only when temperature is fixed. In this scenario, temperature is changing, so Boyle's Law is inapplicable. The correct framework is Gay-Lussac's Law (P/T = constant at fixed volume), which is the natural extension of Charles' Law to rigid containers. This question targets a common confusion: students sometimes apply the wrong law because they remember 'gas + pressure' without checking which variable is held constant.

Question 3

A gas compressed to half its original volume at constant temperature will have twice its original pressure.

• T. True
• F. False

Answer: True

This is a direct application of Boyle's Law: PV = constant (at fixed temperature and fixed amount of gas). If V is halved, then P must double to keep the product PV constant. The intuition is that the same number of molecules now occupy half the space, so they collide with the walls twice as often per unit area, doubling the pressure.

Question 4

Charles' Law predicts that a gas at 0°C has zero volume.

• T. True
• F. False

Answer: False

This is the Celsius trap. 0°C is NOT absolute zero — it is 273 K. Charles' Law (V/T = constant with T in Kelvin) predicts zero volume only at 0 K (absolute zero, −273°C), where molecular motion theoretically ceases. A gas at 0°C still has substantial thermal energy and a nonzero volume. The error reveals exactly why Kelvin is required: using Celsius produces nonsensical predictions because 0°C does not represent the absence of thermal energy.

Question 5

Why must temperature be expressed in Kelvin rather than Celsius when applying Charles' Law?

Model answer: Charles' Law states that volume is directly proportional to absolute temperature (V/T = constant). This proportionality only holds when temperature is measured from true zero — the point of zero thermal energy (0 K, or −273°C). The Kelvin scale starts at this absolute zero. Celsius is an offset scale where 0°C = 273 K, so ratios of Celsius temperatures don't reflect ratios of thermal energy. Doubling from 10°C to 20°C does not double the thermal energy — it corresponds to only a 3.6% increase in Kelvin.

The deeper point is that Charles' Law is a statement about the relationship between molecular kinetic energy and volume. Kinetic energy scales with absolute temperature, not Celsius temperature. Only when you use Kelvin does 'twice the temperature' mean 'twice the thermal energy' — and therefore predict 'twice the volume.' Any gas law involving T as a direct proportionality requires Kelvin.