Chapter 11 · Gases
11.5Charles's Law: Volume and Temperature
11 min · two checks
Predict
A gas is heated from 200 K to 400 K at constant pressure. What happens to its volume?
The idea
- Apply Charles’s law in kelvin.
- Explain why Celsius must not be used directly.
Warm a gas and the particles move faster. If the pressure is allowed to stay constant, the gas expands until the more violent collisions are spread over a larger wall area and the pressure is back where it was. Volume is directly proportional to kelvin temperature: V₁/T₁ = V₂/T₂. A graph of volume versus temperature in °C hits zero volume near −273 °C, which is 0 K. That intercept is one of the reasons the absolute scale exists.
Never insert Celsius into Charles’s law. A temperature of 10 °C is not “twice” 5 °C in any kinetic sense; 283 K is barely warmer than 278 K. Convert first, compute, and if the problem wants °C, convert back after. If the volume rose, the kelvin temperature rose. Negative volumes and negative kelvin temperatures are algebra errors.
Keep these
- V₁/T₁ = V₂/T₂ at constant P and n.
- Temperature must be in kelvin.
- Volume and absolute temperature rise together.
Worked path
A gas occupies 650 mL at 22 °C. What volume does it occupy at 87 °C if pressure is constant?
Observe
T₁ = 295 K, T₂ = 360 K. Volume should increase.