Calculate volume or temperature using Charles's Law: V₁/T₁ = V₂/T₂. Free online thermodynamics calculator for ideal gas law calculations with temperature and volume relationships.
Calculate volume or temperature using V₁/T₁ = V₂/T₂
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Charles's Law is one of the fundamental gas laws in thermodynamics, describing how the volume of a gas changes with temperature when pressure remains constant. Named after French scientist Jacques Charles, this law states that for a given amount of gas at constant pressure, volume is directly proportional to absolute temperature (in Kelvin). Whether you're studying physics, chemistry, engineering, or working with gases, understanding Charles's Law is essential. Our Charles's Law Calculator makes it easy to calculate volume or temperature using the formula: V₁/T₁ = V₂/T₂.
Charles's Law is part of the ideal gas law family and is crucial for understanding gas behavior. When you heat a gas, its particles move faster and spread out, increasing the volume. When you cool a gas, its particles move slower and come closer together, decreasing the volume. This relationship is linear when temperature is measured in Kelvin, making it perfect for calculations involving gas expansion and compression at constant pressure.
Our Charles's Law Calculator is designed for simplicity and accuracy. Follow these steps to get your calculation:
The calculator uses Charles's Law formula: V₁/T₁ = V₂/T₂
You can rearrange this formula to solve for any variable:
Important: All temperature calculations are performed using absolute temperature (Kelvin). The calculator automatically converts between Celsius, Fahrenheit, and Kelvin, but the law requires absolute temperature for accuracy.
Charles's Law is expressed mathematically as:
V₁/T₁ = V₂/T₂
Where: V = volume, T = absolute temperature (Kelvin), subscripts 1 and 2 refer to initial and final states
Charles's Law states that the volume of a given amount of gas is directly proportional to its absolute temperature when pressure and amount of gas remain constant. This means:
Charles's Law requires absolute temperature because the relationship is based on the fact that volume is proportional to kinetic energy. At absolute zero (0 K), particles would theoretically have no motion, so volume would be zero. Using Kelvin ensures the proportionality constant is meaningful. Using Celsius or Fahrenheit would give incorrect results because their zero points don't correspond to absolute zero.
Charles's Law calculations are used in countless real-world scenarios across various fields:
Our calculator supports various units for volume and temperature:
Conversion Formulas:
Tip: The calculator automatically handles all temperature conversions, converting inputs to Kelvin for calculations and then converting results back to your selected unit.
A gas occupies 2.0 L at 20°C. What will be its volume at 80°C if pressure remains constant?
V₁ = 2.0 L, T₁ = 20°C = 293.15 K, T₂ = 80°C = 353.15 K
V₂ = V₁ × T₂ / T₁ = 2.0 L × 353.15 K / 293.15 K = 2.41 L
The gas expands from 2.0 L to 2.41 L as temperature increases
A gas occupies 500 mL at 25°C. If it is cooled to 250 mL at constant pressure, what is the final temperature?
V₁ = 500 mL, T₁ = 25°C = 298.15 K, V₂ = 250 mL
T₂ = V₂ × T₁ / V₁ = 250 mL × 298.15 K / 500 mL = 149.08 K = -124.07°C
The gas cools significantly as its volume is halved
A gas at 100°C has a volume of 3.5 L. What was its initial volume at 0°C if pressure was constant?
T₁ = 0°C = 273.15 K, V₂ = 3.5 L, T₂ = 100°C = 373.15 K
V₁ = V₂ × T₁ / T₂ = 3.5 L × 273.15 K / 373.15 K = 2.56 L
The gas contracted from 3.5 L to 2.56 L as it cooled
Air in a balloon at 20°C occupies 1000 m³. What volume will it occupy when heated to 80°C (typical operating temperature)?
V₁ = 1000 m³, T₁ = 20°C = 293.15 K, T₂ = 80°C = 353.15 K
V₂ = V₁ × T₂ / T₁ = 1000 m³ × 353.15 K / 293.15 K = 1204.6 m³
The balloon expands by about 20% when heated, creating the lift needed for flight
Charles's Law is one of several fundamental gas laws. Understanding how they relate helps in comprehensive gas calculations:
Charles's Law is a special case of the Ideal Gas Law when pressure and amount of gas are constant. It's essential for understanding how gases behave when only temperature changes.
Understanding Charles's Law has practical applications in daily life:
Charles's Law states that the volume of a gas is directly proportional to its absolute temperature when pressure and amount of gas remain constant. It applies to ideal gases when pressure doesn't change during the temperature change. The formula is V₁/T₁ = V₂/T₂, where temperatures must be in Kelvin.
Kelvin is the absolute temperature scale where zero represents absolute zero (no molecular motion). Charles's Law is based on the relationship between volume and kinetic energy, which depends on absolute temperature. Using Celsius or Fahrenheit would give incorrect results because their zero points don't correspond to the point where volume would theoretically be zero.
Charles's Law only applies when pressure remains constant. If pressure changes, you need to use the Combined Gas Law (P₁V₁/T₁ = P₂V₂/T₂) or the Ideal Gas Law (PV = nRT) to account for all three variables: pressure, volume, and temperature.
Charles's Law is most accurate for ideal gases (gases that follow the ideal gas law perfectly) at low pressures and moderate temperatures. Real gases deviate from ideal behavior, especially at high pressures or very low temperatures, but the law provides good approximations for many practical applications.
To Kelvin: K = °C + 273.15, or K = (°F + 459.67) × 5/9. From Kelvin: °C = K - 273.15, or °F = K × 9/5 - 459.67. Our calculator automatically handles these conversions, so you can input temperatures in any unit and get results in your preferred unit.
Volume and temperature are directly proportional in Charles's Law. This means if you double the absolute temperature (in Kelvin), the volume doubles. If you halve the temperature, the volume halves. The relationship is linear when graphed with temperature in Kelvin on the x-axis and volume on the y-axis.
According to Charles's Law, at absolute zero (0 K), the volume would theoretically be zero. However, this is a theoretical limit - real gases condense to liquids or solids before reaching absolute zero. Volume and temperature must both be greater than zero for practical calculations.
Charles's Law is a special case of the Ideal Gas Law (PV = nRT). When pressure (P) and amount of gas (n, number of moles) are constant, the Ideal Gas Law simplifies to V/T = constant, which is Charles's Law. Both laws describe gas behavior, with the Ideal Gas Law being more general.
Understanding Charles's Law and the relationship between volume and temperature is fundamental to thermodynamics and gas physics. Our Charles's Law Calculator simplifies these calculations, making it easy to solve problems involving gas expansion and contraction at constant pressure.
Whether you're studying gas laws, designing thermal systems, or understanding everyday phenomena like hot air balloons, this calculator provides accurate results with support for multiple units and automatic temperature conversions. Ready to explore more thermodynamics concepts? Check out our other calculators like the Specific Heat Calculator for heat energy calculations, or use our Relative Humidity Calculator for understanding air properties and humidity relationships.
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