9.4 Charles's and Gay-Lussac's Laws
Notes
These laws relate temperature to volume or pressure. Temperatures must be in kelvins.
- Charles's law (constant P): volume is directly proportional to temperature. $\displaystyle \frac{V_1}{T_1} = \frac{V_2}{T_2}$.
- Gay-Lussac's law (constant V): pressure is directly proportional to temperature. $\displaystyle \frac{P_1}{T_1} = \frac{P_2}{T_2}$.
- Example: 2.00 L at 27 °C (300 K) heated to 127 °C (400 K): $\displaystyle V_2 = 2.00 \times \frac{400}{300} = 2.67$ L.
- Using °C gives wrong answers: doubling the Celsius temperature does not double the volume.
Practice
A gas has a volume of 3.0 L at 300 K. At constant pressure, what is its volume at 150 K?
$\displaystyle V_2 = 3.0 \times \frac{150}{300} = 1.5$ L.
A sealed can has a pressure of 1.50 atm at 300 K. What is the pressure at 450 K?
$\displaystyle P_2 = 1.50 \times \frac{450}{300} = 2.25$ atm.
A balloon holds 2.00 L at 27 °C. At constant pressure, it is heated to 127 °C. What is the new volume?
Convert to kelvins: 300 K and 400 K. $\displaystyle V_2 = 2.00 \times \frac{400}{300} = 2.67$ L. 9.41 L comes from wrongly using °C.
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