20
0.033333
L/K
2
100
%
20
0.033333
L/K
2
100
%
Charles's Law Calculator solves the direct proportionality between gas volume and absolute temperature at constant pressure: V₁/T₁ = V₂/T₂. Enter the initial volume and temperature, then provide either the final temperature or final volume to calculate the other. Named after Jacques Charles who first noted this relationship in the 1780s, this law explains why hot air balloons rise and why tires expand in summer.
Charles's law is one of the three foundational gas laws and demonstrates that gas volume expands linearly with absolute temperature. It played a crucial role in the development of the Kelvin temperature scale and our understanding of absolute zero.
Charles's law states that at constant pressure, the volume of a fixed amount of gas is directly proportional to its absolute temperature:
$$\frac{V_1}{T_1} = \frac{V_2}{T_2} = k \text{ (constant)}$$
Solving for the unknown:
$$V_2 = V_1 \times \frac{T_2}{T_1} \qquad T_2 = T_1 \times \frac{V_2}{V_1}$$
The proportionality constant \(k = V/T = nR/P\) depends on the amount of gas and the pressure. This law implies that gas volume is zero at absolute zero (0 K = -273.15°C), which historically helped establish the concept of absolute temperature. Of course, real gases liquefy and solidify before reaching absolute zero, so the law doesn't literally predict zero volume.
The percentage change shows how much the solved variable changed relative to its initial value, giving a quick assessment of the magnitude of the effect.
The calculated value gives the final volume or temperature. The V/T constant is the proportionality constant for this specific gas sample at this pressure. The percentage change shows the relative increase or decrease. Since V and T are directly proportional, doubling the absolute temperature doubles the volume. Note that temperatures must be in Kelvin — using Celsius leads to incorrect results because 0°C is not absolute zero.
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Doubling the temperature from 300 K to 600 K at constant pressure doubles the volume from 10 L to 20 L, demonstrating the direct proportionality of Charles's law.
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Halving the volume from 5 L to 2.5 L at constant pressure requires halving the absolute temperature from 400 K to 200 K (-73°C).
Charles's law states that at constant pressure, the volume of a fixed amount of gas is directly proportional to its absolute temperature: V₁/T₁ = V₂/T₂. When temperature doubles (in Kelvin), volume doubles. It was first observed by Jacques Charles around 1787 and published by Joseph Gay-Lussac in 1802.
Heating the air inside a balloon increases its temperature, which by Charles's law increases its volume. The same mass of air now occupies a larger volume, making it less dense than the surrounding cooler air. This density difference creates buoyancy (Archimedes' principle), causing the balloon to rise.
Charles's law is a proportionality relationship (V ∝ T). Proportionality requires a scale that starts at zero. At 0 K, an ideal gas would theoretically have zero volume. Using Celsius (where 0°C is arbitrary) would incorrectly predict negative volumes or wrong ratios. For example, going from 10°C to 20°C is NOT a doubling of temperature.
Absolute zero (0 K = -273.15°C) is the theoretical temperature at which an ideal gas would have zero volume and zero pressure. Charles's law helped establish this concept. In reality, no substance can reach exactly absolute zero (Third Law of Thermodynamics), and real gases liquefy before reaching it.
As temperature increases, the air inside tires expands according to Charles's law (and Gay-Lussac's law since the tire is somewhat rigid). This increases the tire pressure and can cause overinflation. Tire pressure typically increases by about 1 psi for every 5.5°C (10°F) temperature increase.
Charles's law requires: (1) constant pressure (isobaric process), (2) a fixed amount of gas, and (3) ideal gas behavior. In practice, atmospheric pressure processes (open containers) and slow heating/cooling of gas samples are good approximations.
Charles's law is a special case of the ideal gas law (PV=nRT). When P and n are constant, V = (nR/P)T, showing V is directly proportional to T with proportionality constant k = nR/P. This confirms V/T = constant when P and n don't change.
Since volume increases with temperature at constant pressure (Charles's law) but mass stays the same, the gas density (mass/volume) decreases. This is why hot air rises — it is less dense than cooler surrounding air. Gas density is inversely proportional to absolute temperature: ρ = PM/(RT).
Solar heating warms air near the ground, causing it to expand (Charles's law) and become less dense. This warm air rises (convection), cools at higher altitude, and may form clouds. This thermal convection cycle drives weather patterns, sea breezes, and atmospheric circulation.
Charles's law relates volume and temperature at constant pressure (V₁/T₁ = V₂/T₂). Gay-Lussac's law relates pressure and temperature at constant volume (P₁/T₁ = P₂/T₂). Both show direct proportionality with absolute temperature but for different gas properties. Together with Boyle's law, they form the combined gas law.
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