Charles's Law
The Volume-Temperature Relationship at Constant Pressure.
While Boyle investigated pressure and volume, French scientist Jacques Charles (a pioneer in hot air ballooning) investigated how gases behave when heated. In 1787, he formulated the law that elegantly connects the volume of a gas to its temperature.
1. Statement & Mathematical Formula
Charles's Law states: At constant pressure, the volume of a fixed mass of gas is directly proportional to its absolute temperature.
When you heat a gas, the kinetic energy of the molecules increases. They hit the walls of the container harder and more frequently. To maintain a constant pressure, the volume of the container must expand.
$$\frac{V}{T} = k \quad (\text{where } k \text{ is a constant})$$
Temperature ($T$) must ALWAYS be in Kelvin ($K$). If you plug Celsius ($^\circ C$) into $V_1/T_1 = V_2/T_2$, your answer will be completely wrong!
The Problem-Solving Equation:
If a gas undergoes a change in conditions from state 1 to state 2 at constant pressure:
2. Graphical Representation (Isobars)
Graphs drawn at a constant pressure are called Isobars (iso = same, bar = pressure). The relationship $V = kT$ is the equation of a straight line ($y = mx$) passing through the origin.
Volume vs Temp (Kelvin)
Straight line through origin.
P₂ > P₁ (Higher P = Lower slope)
Volume vs Temp (Celsius)
Extrapolates to -273.15°C at V=0.
3. The Discovery of Absolute Zero
Charles discovered that for every $1^\circ C$ rise or fall in temperature, the volume of a gas expands or contracts by $\frac{1}{273.15}$ of its volume at $0^\circ C$.
If we cool a gas down, its volume keeps decreasing. According to the formula, if we cool the gas to $-273.15^\circ C$, its volume will theoretically become exactly zero!
Since matter cannot have negative volume, $-273.15^\circ C$ is the lowest possible temperature in the universe. This phenomenon inspired Lord Kelvin to create a new temperature scale starting at this exact point: Absolute Zero ($0 \text{ K}$).
4. Real-Life Applications & Density
Density Relationship
Density ($d$) is Mass ($m$) / Volume ($V$). Since Charles's Law says volume increases as temperature increases, heating a gas causes its density to decrease. Hot gas is lighter than cold gas!
Applications
- Hot Air Balloons: When the burner heats the air inside the envelope, the air expands. Because its volume increases, its density drops below that of the surrounding cool air, causing the balloon to float upwards.
- Shrinking Balloons in Cold: If you take a fully inflated helium or air balloon outside on a freezing winter day, it will noticeably shrink. The drop in temperature causes a proportional drop in volume.
- Baking: Yeast produces $CO_2$ gas. When bread goes into a hot oven, the high temperature causes those trapped gas bubbles to expand rapidly, making the bread rise and become fluffy.
Knowledge Check
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