Jacques Charles: Gases Expand With Temperature at Constant Pressure

After Boyle discovered that pressure and volume are inversely related (PV = constant), physicists wondered: what about temperature?

In 1787, Jacques Charles experimented with gas behavior at different temperatures.

He discovered: at constant pressure, gas volume is proportional to absolute temperature.

Combined with Boyle's Law, Charles's Law unified gas behavior into one elegant principle: the ideal gas law.

The Context

Boyle's Law (1660s): at constant temperature, P×V = constant

Charles observed: but what happens if temperature changes?

Using hydrogen, oxygen, and air, Charles heated gases in sealed containers at constant pressure.

He measured how volume changed.

The Discovery

Charles found linear relationship:

At constant pressure, V/T = constant

Or: V ∝ T (Volume proportional to absolute temperature)

More precisely: V₁/T₁ = V₂/T₂

If temperature doubles, volume doubles (at constant pressure).

The Key: Absolute Temperature

Crucial detail: Charles used absolute temperature (Kelvin), not Celsius.

At 0°C (273 K), gas would theoretically have zero volume (not actually possible—gas liquefies first).

But the linear relationship holds: V = nRT/P (for ideal gas)

Why It Works

Molecular kinetic theory explains Charles's Law:

Higher temperature → gas molecules move faster

Faster molecules exert more pressure on container walls

To maintain constant pressure, volume must increase (container expands)

Volume increase exactly proportional to temperature increase

This emerges from statistical mechanics naturally.

Applications

Charles's Law explains:

Hot air balloons: Heat air inside balloon, density decreases, balloon rises

Tire pressure: Car tires have higher pressure when hot (driving heats tire)

Thermometers: Gas bulbs expand with temperature—can measure temperature from volume

Breathing: Body temperature variations affect lung volume slightly

Cooking: Ovens use thermal expansion (measuring temperature indirectly)

Combined with Boyle's Law

Boyle: PV = constant (at fixed T)

Charles: V/T = constant (at fixed P)

Combined: PV/T = constant

Or: PV = nRT

The ideal gas law—unifying all gas relationships in one equation.

The Ideal Gas Law

PV = nRT

Where:

• P = pressure
• V = volume
• n = amount of gas (moles)
• R = gas constant
• T = absolute temperature

This single equation describes all ideal gas behavior.

Real Gases

Real gases approximate ideal behavior at:

• Low pressure (molecules far apart)
• High temperature (molecules moving fast)

At high pressure or low temperature, real gases deviate (molecules interact).

But ideal gas law remains excellent approximation for most conditions.

Charles's Experiments

Charles used "Charles's apparatus":

• Gas in tube, open at bottom
• Mercury barometer to measure pressure (keeping constant)
• Heat source to vary temperature
• Measure volume change

Elegant simplicity. Clear demonstration of proportionality.

Charles's Life

Jacques Charles (1746-1823):

• French physicist and inventor
• Pioneer of hydrogen balloon flights (1783)
• First balloon to reach significant altitude
• Professor of physics in Paris

He contributed to both experimental physics and engineering.

Hydrogen Balloons

Before hot air balloons, Charles used hydrogen balloons:

Hydrogen is lighter than air.

A hydrogen-filled balloon rises.

Charles pioneered this technology—his August 1783 balloon flight was major event.

(Hot air balloons, invented independently, flew weeks earlier.)

Absolute Zero Prediction

Charles's Law suggests: V → 0 as T → 0 K

This predicted absolute zero—temperature at which gas volume becomes zero.

Later, thermodynamics confirmed absolute zero at T = 0 K = -273.15°C.

Charles's extrapolation from gas law predicted this fundamental temperature limit.

Limitations

Charles's Law (like Boyle's) applies to ideal gases.

Real gases:

• Condense to liquid at low temperature (volume drops sharply)
• Deviate at high pressure
• Have molecular size effects

But ideal gas law remains excellent approximation in most practical conditions.

Modern Gas Laws

Modern thermodynamics refined gas laws:

Van der Waals equation: Accounts for molecular size and intermolecular forces

Virial equation: Series expansion accounting for deviations

But for engineering calculations, ideal gas law (PV = nRT) remains standard.

Historical Timeline

• 1660s: Boyle's Law (P and V)
• 1787: Charles's Law (V and T)
• 1811: Avogadro's Law (V and amount of gas)
• 1873: Van der Waals refines ideal gas law

Gradual development from observation to universal equation.

Thermodynamic Significance

Charles's Law reveals fundamental truth:

Temperature measures molecular motion.

Higher temperature → faster molecules → higher pressure or volume (depending on constraints)

This connection between temperature and molecular behavior is central to statistical mechanics.

Jacques Charles and Hydrogen Balloons

Jacques Charles (1746-1823) was French physicist and inventor. In 1783, months before the Montgolfier brothers' hot air balloon, Charles pioneered hydrogen balloon flights. Hydrogen is 14 times lighter than air—filled balloon rises. Charles designed the first hydrogen balloon (August 27, 1783), flying from Paris to countryside. This was revolutionary: humans first achieved flight, powered by lifting gas.

Charles's gas law emerged from scientific curiosity about gas behavior. His law directly connects to his balloon work: understand gas expansion with temperature, predict lift and performance.

His contributions span both theory (gas law) and engineering (balloon technology). He exemplifies practical physicist—bridging experiment and application.

Absolute Temperature Necessity

Critical insight: Charles used absolute temperature (Kelvin), not Celsius.

At 0°C (273 K), his formula predicts V → 0. Physically impossible (gas can't have zero volume), but mathematically correct for ideal gas. As temperature approaches absolute zero, volume approaches zero. Temperature cannot go below 0 K; this is nature's temperature limit.

Charles's law predicted this absolute zero—later confirmed by thermodynamics (0 K = -273.15°C). His simple proportionality revealed fundamental temperature constraint.

This is profound: empirical observation of gas behavior predicted the lowest possible temperature in universe. Modern physics confirms 0 K is unreachable limit (third law of thermodynamics).

Gas Mixtures and Dalton's Law

Charles's Law applies to pure gases. For mixtures:

Dalton's Law of Partial Pressures: Total pressure = sum of partial pressures from each gas component.

P_total = P₁ + P₂ + P₃ + ...

Combined with Charles's Law:

• Each component: V_i/T = constant (at fixed P_i)
• Total volume: V/T = constant (at fixed P)

Applies to air (mixture of N₂, O₂, Ar, CO₂). Breathing, weather, engines—all involve gas mixtures.

Real Gas Deviations

Charles's Law (ideal gas law) assumes:

• Gas molecules are point particles (zero volume)
• No forces between molecules
• Perfectly elastic collisions

Real gas deviations:

• High pressure: Molecule size matters; deviations large
• Low temperature: Intermolecular forces dominate; liquid condenses
• Near phase transitions: Ideal gas law fails completely

Van der Waals equation accounts for these: (P + a n²/V²)(V - nb) = nRT

Additional terms account for molecule size (nb) and intermolecular forces (an²/V²). For low pressures and high temperatures, Van der Waals reduces to ideal gas law—showing ideal gas law is limit case of more complete theory.

Historical Gas Law Development

• 1660: Boyle discovers P and V inversely related (PV = constant at fixed T)
• 1787: Charles discovers V and T proportional (V/T = constant at fixed P)
• 1811: Avogadro proposes equal volumes contain equal molecular numbers (explains why combining ratios of gases are simple integers)
• Combined: PV = nRT (ideal gas law)
• 1873: Van der Waals refines for real gases

Gradual development from empirical observations to universal equation. Each physicist added piece; together they explained gas behavior completely.

Modern Applications and Engineering

Charles's Law enables:

Internal combustion engines: Gasoline + air mixture ignites, heating gas. Volume increases (at constant pressure) pushing piston. Controlled expansion drives engine. Power depends on temperature (hotter fire → more expansion → more force).

Pneumatic tools: Compressed air expands, powering tools. Tool output depends on volume and temperature. Cold air = less expansion = less power. Air dryers used in pneumatic systems to prevent temperature loss.

HVAC systems: Heating/cooling changes air temperature, causing expansion/contraction. Ductwork designed accounting for thermal expansion. Thermal stresses in ductwork cause noises (expansion/contraction sounds) in buildings.

Cooking: Oven temperature affects gas expansion. Ovens are designed to reach stable temperature, maintaining gas volume. Temperature sensing relies on gas expansion (older ovens used gas-filled thermometers).

Scuba diving: Diver's lungs receive compressed air (high pressure). As diver rises, pressure decreases. Air expands (Charles's Law, at decreasing external pressure). Diver must exhale to prevent lung rupture.

Source: Charles, Jacques Alexandre César (1787) — Original experiments (referenced in historical records; few original papers survive)

Source: Gay-Lussac, Joseph Louis (1809) — Extended Charles's work, confirmed V/T relationship

Source: Clapeyron, Émile (1834) — "Mémoire sur la puissance motrice de la chaleur" (formulated ideal gas law equation)

Frequently Asked Questions

Q: Why doesn't gas have zero volume at 0 K?
A: Physically, it doesn't. Gases liquefy before reaching 0 K (depending on pressure and gas type). Hydrogen liquefies at 20 K; helium at 4.2 K. At these temperatures, ideal gas law fails—gas is no longer gas; it's liquid or solid. Charles's Law (and ideal gas law) strictly applies only to gas phase. It breaks down at phase transitions.

Q: Why do airplanes require decompression when ascending?
A: Atmospheric pressure decreases with altitude exponentially. At aircraft cabin altitude (~10,000 m without pressurization), pressure is ~0.26 atmospheres. Charles's Law says gas expands at lower pressure. Without pressurization, air in cabin would expand excessively, straining structure. Solution: pressurized cabin maintains ~0.8 atmosphere inside, comfortable for passengers. Without pressurization, pressure differential (outside vs. inside) would cause structural failure; cabin would rupture.

Q: How do we measure temperature using gas thermometers?
A: Gas thermometer uses Charles's Law. Known volume of gas at known pressure. Heat the gas (temperature changes). Measure volume change (or pressure change at constant volume). From V/T = constant, calculate new temperature. Old mercury and alcohol thermometers used thermal expansion of liquid (same principle: volume changes with temperature). Gas thermometers are more accurate (wider temperature range, better linearity) but less convenient (bulkier).

Q: Why do car tire pressures increase when tires get hot?
A: Driving heats tires (friction, flexing). Charles's Law (or ideal gas law): at constant tire volume, temperature increase causes pressure increase. Pressure ∝ Temperature (at fixed V and n). Hot tires have higher pressure than cold tires. Gas station measurements should be done on cold tires for consistent readings. Hot tire pressure reading would be artificially high, underestimating true air amount.

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