Charles' Law Calculator

Calculate gas volume and temperature relationships at constant pressure using Charles' Law

Charles' Law Analysis

L

Starting volume of gas

°C

Starting temperature of gas

L

Final volume of gas

°C

Final temperature of gas

Charles' Law Results

1.832 L
Final Volume (V₂)
0.006708
V/T Ratio (L/K)
✓ Ratio verified

Initial State

Volume:2 L
Temperature:298.15 K
V/T Ratio:0.006708 L/K

Final State

Volume:1.832 L
Temperature:273.15 K
V/T Ratio:0.006708 L/K

Charles' Law Formula

Relationship: V₁/T₁ = V₂/T₂ (at constant pressure)

Calculation: V₂ = V₁ × T₂/T₁ = 2 × 273.1/298.1 = 1.832 L

Note: Temperature must be in Kelvin for calculations

Real-World Examples

Hot Air Balloon

V₁ = 2500 L, T₁ = 15°C

V₂ = 2850 L, T₂ = 80°C

Heating air for balloon flight

Beach Ball (Hot to Cold)

V₁ = 2 L, T₁ = 35°C

V₂ = 1.87 L, T₂ = 15°C

Ball cooling in AC room

Liquid Nitrogen Demo

V₁ = 0.5 L, T₁ = 25°C

V₂ = 0.07 L, T₂ = -196°C

Balloon in liquid nitrogen

Car Tire (Summer to Winter)

V₁ = 50 L, T₁ = 30°C

V₂ = 47.5 L, T₂ = -10°C

Seasonal tire pressure change

Gas Thermometer

V₁ = 0.03 L, T₁ = 22°C

V₂ = 0.062 L, T₂ = 337°C

Volume-based temperature measurement

Syringe Experiment

V₁ = 10 L, T₁ = 20°C

V₂ = 11.2 L, T₂ = 60°C

Heating gas in syringe

Charles' Law Reference

Basic Formula

V₁/T₁ = V₂/T₂

At constant pressure

Direct Proportionality

V ∝ T (absolute temperature)

Volume increases with temperature

Key Conditions

  • • Constant pressure (isobaric)
  • • Fixed amount of gas
  • • Ideal gas behavior
  • • Temperature in Kelvin

Applications

  • • Hot air balloons
  • • Gas thermometers
  • • Tire pressure changes
  • • Liquid nitrogen demos

Understanding Charles' Law

What is Charles' Law?

Charles' Law describes the relationship between the volume and temperature of a gas when pressure remains constant. Named after Jacques Charles, it states that volume is directly proportional to absolute temperature.

Mathematical Relationship

Charles' Law: V₁/T₁ = V₂/T₂

Proportionality: V ∝ T (at constant P)

Linear form: V = kT (where k is constant)

Key Requirements

  • Constant Pressure: Pressure must remain unchanged (isobaric process)
  • Fixed Gas Amount: Number of moles must be constant
  • Absolute Temperature: Temperature must be in Kelvin scale
  • Ideal Gas: Works best for gases behaving ideally

Real-World Applications

Hot Air Balloons

Heating air increases its volume and decreases density, creating buoyancy that lifts the balloon. Charles' Law explains the volume-temperature relationship.

Seasonal Tire Changes

Tire pressure appears to drop in winter and rise in summer due to temperature-volume relationships described by Charles' Law.

Gas Thermometry

Constant-pressure gas thermometers use Charles' Law to measure temperature by observing volume changes of a gas.

Limitations

  • • Valid only for ideal gases or real gases under moderate conditions
  • • Pressure must remain truly constant throughout the process
  • • Gas amount (moles) must not change
  • • Extreme temperatures or pressures may cause deviations

Solving Charles' Law Problems

Step-by-Step Method

  1. 1. Identify initial and final conditions (V₁, T₁, V₂, T₂)
  2. 2. Convert all temperatures to Kelvin (T = °C + 273.15)
  3. 3. Verify pressure remains constant throughout process
  4. 4. Apply Charles' Law formula: V₁/T₁ = V₂/T₂
  5. 5. Solve for the unknown variable algebraically
  6. 6. Check that the V/T ratio is constant

Example Problem:

A gas occupies 2.0 L at 25°C. What volume will it occupy at 100°C?

Solution: V₂ = V₁ × T₂/T₁ = 2.0 L × 373.15 K / 298.15 K = 2.50 L

Common Mistakes to Avoid

Temperature Units

Always convert to Kelvin! Celsius or Fahrenheit will give incorrect results.

Pressure Changes

Charles' Law only applies when pressure is constant. Verify this condition.

Volume Units

Ensure consistent volume units throughout the calculation.

Quick Checks

  • • Higher temperature → larger volume
  • • Lower temperature → smaller volume
  • • V/T ratio should be the same for both states
  • • Results should make physical sense