Charles' Law Calculator
Calculate gas volume and temperature relationships at constant pressure using Charles' Law
Charles' Law Analysis
Starting volume of gas
Starting temperature of gas
Final volume of gas
Final temperature of gas
Charles' Law Results
Initial State
Final State
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. Identify initial and final conditions (V₁, T₁, V₂, T₂)
- 2. Convert all temperatures to Kelvin (T = °C + 273.15)
- 3. Verify pressure remains constant throughout process
- 4. Apply Charles' Law formula: V₁/T₁ = V₂/T₂
- 5. Solve for the unknown variable algebraically
- 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