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Gay Lussac's Law Calculator

The calculator will calculate the initial and final values for pressure and temperature by employing Gay Lussac’s law equation.

To calculate:

Initial temperature (p₁):

Pa ▾

Initial pressure (T₁):

K ▾

Final temperature (p₂):

Pa ▾

Final pressure (T₂):

K ▾

Amount of gas (V):

m³ ▾

Volume (n):

mol

Gas Mole (R):

J⋅K⁻¹⋅mol⁻¹

Related

Gay-Lussac’s Law Calculator

An online free Gay-Lussac’s Law calculator helps you instantly determine gas parameters in an isochoric (constant volume) process. It allows you to analyze the behavior of gas pressure and temperature while keeping the volume constant.

Gay-Lussac’s Law

In 1802, Sir Gay-Lussac proposed a law describing gas expansion:

Statement:

“For an ideal gas, the pressure of the gas is directly proportional to its temperature when the volume is held constant.”

This calculator can analyze pressure and temperature changes instantly.

Gay-Lussac’s Law Formula

Mathematically:

$$ \frac{P_{1}}{T_{1}} = \frac{P_{2}}{T_{2}} $$

P₁ = Initial Pressure
T₁ = Initial Temperature
P₂ = Final Pressure
T₂ = Final Temperature

You can also calculate moles of gas and total volume using the Gay-Lussac’s Law calculator. For pressure-volume relationships, refer to the Boyle’s Law calculator, and for temperature-volume relations, use the Charles’s Law calculator.

Derivation of Gay-Lussac’s Law

Using Boyle’s and Charles’s laws:

Boyle’s Law: $$ P_1 \times V_1 = P_2 \times V $$

Charles’s Law: $$ T_1 \times V_2 = T_2 \times V $$

Equating the volumes:

$$ \frac{P_1 \times V_1}{P_2} = \frac{T_2 \times V_2}{T_1} = k $$

Hence: $$ P \propto T \quad \text{or} \quad P = k \times T $$

Real-World Applications

Firing a Bullet:

The explosion generates high pressure propelling the bullet. Use the calculator to estimate instantaneous pressure.

Tire Pressure vs Temperature:

In a tire, pressure increases with temperature proportionally and decreases when cooled.

Air in a Balloon:

Lowering temperature reduces the pressure inside a balloon, illustrating Gay-Lussac’s Law.

Heating an Aerosol Can:

Heating increases internal pressure due to the direct relationship between temperature and pressure.

Example #01

Find the final pressure given:

T₁ = 23 K
P₁ = 12 Pa
T₂ = 4 K

Solution:

$$ \frac{P_1}{T_1} = \frac{P_2}{T_2} $$

$$ \frac{12}{23} = \frac{P_2}{4} $$

$$ P_2 = \frac{4 \times 12}{23} = 7.66 \text{ Pa} $$

Example #02

Find the initial pressure given:

T₁ = 23 K
P₂ = 9 Pa
T₂ = 34 K

Solution:

$$ \frac{P_1}{23} = \frac{9}{34} $$

$$ P_1 = \frac{9 \times 23}{34} = 6.08 \text{ Pa} $$

How Gay-Lussac’s Law Calculator Works

Input:

Select the parameter to calculate.
Enter all known values (pressure, temperature, etc.).
Choose appropriate units for each parameter.
Click Calculate to obtain results.

Output:

Initial and final pressures
Initial and final temperatures
Volume and moles of gas if required

FAQ’s

Why Does Temperature Decrease with Pressure?

Temperature and pressure are directly related in a fixed volume. However, in the atmosphere, temperature increase causes gas expansion, lowering pressure locally.

Does Pressure Increase with Altitude?

No, atmospheric pressure decreases with altitude due to reduced air density and gravitational pull.

Why Is Pressure Higher in the Lower Atmosphere?

Lower altitudes generally have higher pressure due to denser air and heat variations from solar heating.

Is High Pressure Hot or Cold?

High pressure often occurs in cooler regions where gas molecules are less spread out.

Is Rain Associated with High or Low Pressure?

Rain occurs in low-pressure conditions where water vapor condenses and precipitates.

References

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