Charles's Law Notes

The Gas Laws (Continued)

Lesson 3: Charles's Law

Lesson Objectives

• State the relationship between volume and temperature of a fixed mass of gas at constant pressure: $V \propto T$ or $\frac{V<em>1}{T</em>1} = \frac{V<em>2}{T</em>2}$
• Carry out calculations using the relationship between volume and temperature.

Volume and Temperature

• Volume and temperature are directly proportional when temperature is measured in Kelvin.
• To convert Celsius to Kelvin, the formula is: $K = °C + 273$
• Absolute zero is -273°C.

Volume and Temperature Relationship

• If temperature increases:
  • Particles move faster.
  • Particles collide harder and more often with the piston.
  • The piston is pushed further up, increasing the volume.

Charles’s Law

• For a fixed mass of gas at a constant pressure, the volume of the gas is directly proportional to the temperature (in Kelvin).
• If the temperature doubles, the volume doubles; if the temperature triples, the volume triples, etc.
• Mathematical representations:
  • $V \propto T$
  • $\frac{V}{T} = constant$
  • $\frac{V<em>1}{T</em>1} = \frac{V<em>2}{T</em>2}$

Examples

• A fully inflated balloon at room temperature.
• The same balloon with the same amount of air after liquid nitrogen is poured over it, demonstrating the volume decrease with temperature decrease.

Practice Problems

• Problem 1: Some gas in a fixed volume container is at a temperature of 27°C and a pressure of 100kPa. If the gas is heated to a temperature of 177°C, what will its pressure be? (Remember to convert to Kelvin).
• Problem 2: Hot air in a strong can is at a temperature of 77°C and a pressure of 120kPa. The can is then left in a fridge so that the pressure of the air reduces to 96kPa. What is the temperature of the fridge, in K and °C?