7.018305
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1
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3,709.500275
3,699.825252
0.997392
7.018305
0
1
0
3,709.500275
3,699.825252
0.997392
The Combined Gas Law Calculator merges Boyle's, Charles's, and Gay-Lussac's laws into a single equation: P₁V₁/T₁ = P₂V₂/T₂. This powerful relationship tracks how a fixed amount of gas behaves when pressure, volume, and temperature all change simultaneously.
The combined gas law is indispensable in atmospheric science, aviation, engine thermodynamics, and any scenario where multiple gas properties change at once. It can solve for any of the six variables when the other five are known.
The combined gas law is written as:
$$\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}$$
This equation holds for a fixed amount of gas (constant n). From the ideal gas law PV = nRT, since n and R are constant:
$$\frac{PV}{T} = nR = \text{constant}$$
Solving for each variable:
$$P_2 = \frac{P_1 V_1 T_2}{T_1 V_2}, \quad V_2 = \frac{P_1 V_1 T_2}{T_1 P_2}, \quad T_2 = \frac{P_2 V_2 T_1}{P_1 V_1}$$
The combined gas law reduces to the individual laws when one variable is held constant:
The ratio PV/T is a conserved quantity for a fixed sample of gas. The calculator displays this ratio for both initial and final states — they should be equal, confirming the amount of gas did not change.
If the initial and final PV/T values differ, gas was either added or removed from the system. All temperatures must be in Kelvin. The combined gas law is especially useful for weather balloon calculations (altitude changes P, T simultaneously) and engine compression strokes (V decreases while T increases).
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A 1-liter balloon at sea level (101325 Pa, 20 °C) expands to about 2.91 L at altitude where pressure drops to 26500 Pa and temperature falls to −50 °C. Despite cooling, the pressure drop dominates.
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Compressing gas 10:1 ratio at 10× pressure increase yields the same temperature (300 K). In practice, adiabatic compression raises temperature much higher because work converts to heat.
The combined gas law, P₁V₁/T₁ = P₂V₂/T₂, relates the initial and final states of a fixed amount of gas when pressure, volume, and temperature all change. It combines Boyle's, Charles's, and Gay-Lussac's laws into one equation.
Use it whenever more than one variable changes. If only P and V change (constant T), Boyle's Law suffices. But if a gas is simultaneously compressed and heated, you need the combined gas law to account for both effects.
No. The combined gas law assumes a fixed amount of gas (constant moles). If gas is added or removed, use the full ideal gas law PV = nRT for each state separately.
PV/T equals nR, where n is moles and R is the gas constant. It represents a conserved quantity for a closed gas system — the same value before and after any process that doesn't add or remove gas.
Pilots and meteorologists use it to predict how air pressure and temperature changes with altitude affect gas volumes. It helps calculate cabin pressurization requirements, fuel tank vapor space, and altimeter corrections.
Yes — P₁ and P₂ must be in the same units (Pa, atm, bar, etc.), V₁ and V₂ in the same units (L, m³, etc.), but T must always be in Kelvin. The units cancel in the ratios, except temperature which requires an absolute scale.
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