20
0.03661
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0.03661
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2
2
20
0.03661
L/K
0.03661
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2
2
The Charles's Law Calculator computes how gas volume changes with temperature at constant pressure: V₁/T₁ = V₂/T₂. Named after Jacques Charles, who discovered in 1787 that gases expand linearly with temperature, this law is essential for understanding thermal expansion of gases, hot air balloons, weather phenomena, and engine thermodynamics.
The law reveals a direct proportionality between absolute temperature and volume — heat a gas and it expands; cool it and it contracts. This calculator solves for any one of the four variables when the other three are known.
Charles's Law states that at constant pressure, the volume of a fixed amount of gas is directly proportional to its absolute temperature:
$$\frac{V_1}{T_1} = \frac{V_2}{T_2}$$
Equivalently:
$$V = kT \quad (\text{constant at fixed } n, P)$$
where k = nR/P from the ideal gas law. Solving for each variable:
$$V_2 = V_1 \times \frac{T_2}{T_1}, \quad T_2 = T_1 \times \frac{V_2}{V_1}$$
The graph of V versus T is a straight line through the origin (when T is in Kelvin). Extrapolating the line to zero volume gives absolute zero (0 K = −273.15 °C), which is how absolute zero was historically estimated.
Temperature must always be in Kelvin. Using Celsius would give incorrect results because Charles's Law requires an absolute scale where zero represents the theoretical absence of thermal energy.
The expansion factor V₂/V₁ equals T₂/T₁, so heating a gas from 300 K to 600 K doubles its volume at constant pressure — a principle exploited in hot air balloons and combustion engines.
A result where V₂ > V₁ means the gas expanded (T₂ > T₁). The V/T ratios should be equal — if they differ, the pressure or amount of gas changed. Remember that all temperatures must be positive Kelvin values; approaching 0 K means the gas would theoretically occupy zero volume (though real gases liquefy first).
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Heating 10 L of gas from 0 °C (273.15 K) to 100 °C (373.15 K) at constant pressure expands it to about 13.66 L — a 36.6% increase.
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If gas expanded from 5 L to 8 L when heated to 480 K, the initial temperature was 300 K (26.85 °C). The ratio 5/300 = 8/480 confirms the relationship.
Charles's Law states that at constant pressure, the volume of a fixed quantity of gas is directly proportional to its absolute temperature (in Kelvin): V₁/T₁ = V₂/T₂. Heating a gas makes it expand; cooling makes it contract.
Because Charles's Law requires an absolute temperature scale. At 0 K, a gas theoretically has zero volume. Using Celsius (where 0 °C is arbitrary) would give meaningless ratios and incorrect results.
Heating air inside the balloon increases its volume (Charles's Law). Since the balloon constrains the volume, some air escapes, reducing the density inside. The lighter balloon then rises because of buoyancy — the surrounding cooler air is denser.
Absolute zero (0 K = −273.15 °C) is the theoretical temperature where gas volume extrapolates to zero. It was first estimated by extending Charles's Law V-vs-T lines backward. In reality, all gases liquefy before reaching 0 K.
It works well at moderate pressures and temperatures well above the boiling point. Near condensation or at very high pressures, intermolecular forces cause deviations. Noble gases like helium follow it most closely.
Charles's Law relates volume and temperature at constant pressure (V/T = k). Gay-Lussac's Law relates pressure and temperature at constant volume (P/T = k). Both show direct proportionality with absolute temperature.
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