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Charles's Law Calculator

Find final volume when temperature changes at constant pressure (use kelvin)

Parameters

m³ⓘ
Kⓘ
Kⓘ
Show Trail

Controls

xⓘ

Calculated Values

Final Volume V₂:
2.67;m32.67;m³
Volume Ratio V₂/V₁:
1.33;1.33;

Examples

Heat gas in balloon

300 K → 400 K, V₁=2 m³.

  • V₂: 2.672.67

Cooling

500 K → 250 K.

  • V₂: 0.500.50

Visualization

Charles's Law — Volume and Absolute Temperature

Charles's law (Jacques Charles, 1780s; published by Gay-Lussac) states that for a fixed amount of gas at constant pressure, volume is directly proportional to absolute temperature: V ∝ T, or V₁/T₁ = V₂/T₂. Temperature must be in kelvin.

From PV = nRT with P and n constant: V = (nR/P)·T, so the slope of V vs T is linear through the origin when extrapolated to T = 0 K. Historical gas thermometry used this linear relation.

Heating a gas in an open container (or flexible balloon) at ~constant atmospheric pressure increases molecular kinetic energy, expansion, and volume. Cooling contracts the gas. At constant P, density ρ ∝ 1/T.

Absolute zero (−273.15 °C = 0 K) is the theoretical temperature where an ideal gas would have zero volume — the intercept of the Charles line. Never use Celsius in V/T ratios: 100 °C is not twice as hot as 50 °C in the thermodynamic sense; 373 K vs 323 K is the correct comparison.

Charles's law is the isobaric (constant pressure) gas law. Combined with Boyle's (isothermal) and Gay-Lussac's (isochoric, P ∝ T), it yields PV = nRT. Isobaric work W = PΔV; heating at constant P requires heat Q = nC_pΔT.

Hot air balloons heat air at ~constant pressure: volume increases, density decreases (ρ = PM/RT), and buoyant force exceeds weight. Aviation uses density altitude — warmer air is less dense, reducing lift.

Key Concepts

  • V₁/T₁ = V₂/T₂ — T must be in kelvin
  • V ∝ T at constant P and n
  • Isobaric process (constant pressure)
  • Extrapolation to absolute zero at 0 K
  • Never use Celsius in gas law ratios
  • Hot air balloon: V↑, ρ↓, buoyancy↑

Real-World Applications

  • Hot air balloons and heated-air furnaces
  • Constant-pressure gas thermometers
  • Engine intake manifold air density (temperature effects)
  • Class 11 gas laws and kelvin scale introduction
  • Aviation density altitude and aircraft performance
  • Expansion joints in bridges and pipelines (related thermal expansion)

Explore Further

More thermodynamics tools

Physics Equations

Charles's Law:
V1T1=V2T2\frac{V_1}{T_1} = \frac{V_2}{T_2}
Solve V₂:
V2=V1T2T1V_2 = V_1 \frac{T_2}{T_1}

Step-by-Step Solution

See how the main results are calculated.

1

Step 1: Constant Pressure

Gas expands when heated at fixed P.

Explanation:

Charles's law: volume proportional to absolute temperature.

2

Step 2: Charles's Law

Equation:

V1T1=V2T2\frac{V_1}{T_1} = \frac{V_2}{T_2}

Explanation:

T must be in kelvin.

3

Step 3: Kelvin Temperatures

Calculation:

T1=300 K,T2=400 KT_1 = 300 \text{ K}, \quad T_2 = 400 \text{ K}

Explanation:

Never use Celsius in gas law ratios without converting.

4

Step 4: Solve V₂

Calculation:

V2=V1T2T1=2×400300=2.6667V_2 = V_1 \frac{T_2}{T_1} = 2 \times \frac{400}{300} = 2.6667

Result:

V2=2.6667V₂ = 2.6667
5

Step 5: Trend

Heating increases volume.

Explanation:

T₂ > T₁ ⇒ V₂ > V₁ at constant pressure.

6

Step 6: Absolute Zero

Extrapolation gives V → 0 at T = 0 K.

Explanation:

Historical basis for kelvin scale.

Frequently Asked Questions (FAQ)

Why kelvin only?

At T=0 K volume should be zero; Celsius zero is arbitrary.

Charles vs Gay-Lussac?

Charles: V∝T at fixed P. Gay-Lussac: P∝T at fixed V.

Negative Celsius in ratio?

Convert to K first — negative Celsius gives wrong ratio.

Does pressure stay exactly constant?

Open container approximates constant P; sealed can change P.

Hot air balloon physics?

Heated air less dense — same P, larger V, buoyancy.

Practice MCQs

  1. Temperature must be in:
  2. Heating gas at constant P:
  3. From 300 K to 600 K, volume at constant P:
  4. Charles law with pressure constant is:
  5. V₁/T₁ equals:
  6. 0 °C in Charles law should be written as:

Related Calculators

These tools connect to the same physics concepts used in this calculator.

First Law of ThermodynamicsCalculate internal energy change ΔU = Q − W from heat and work.Adiabatic ProcessFind P₂ and T₂ for reversible adiabatic ideal gas expansion (Q = 0).Isothermal ProcessCalculate work W = nRT ln(V₂/V₁) and heat for isothermal ideal gas.Boyle's LawCalculate pressure or volume at constant temperature (P₁V₁ = P₂V₂).Error PropagationCombine measurement uncertainties for sums, products, quotients, and powers in experimental formulas.Related Measurement & Uncertainty topic.Maxwell-Boltzmann DistributionCalculate velocity distributions and characteristic velocities for ideal gases using Maxwell-Boltzmann statistics.Related Statistical Physics topic.Projectile MotionCalculate and visualize the path of objects under the influence of gravity.Related Mechanics topic.