GAY-LUSSAC'S LAW CALCULATOR

Gay-Lussac's Law Calculator
(or Pressure Law Calculator)
ALWAYS use absolute temperature with this calculator.
Scroll to the bottom for instructions and 4 examples.
This law is incorrectly named after Joseph Gay-Lussac and was actually
discovered by French inventor and physicist Guillaume Amontons (1663-1705).

Absolute temperature is ALWAYS required with Gay-Lussac's Law.
(either Kelvin or the less common Rankine scale can be used).
For a Temperature Converter, click here.

P₁ P₂
------ = ------
T₁ T₂

The above formula is Gay-Lussac's Law named after the French chemist and physicist Joseph Louis Gay-Lussac (1778 - 1850). The law states that the pressure of a fixed mass of gas at a constant volume is directly proportional to its absolute temperature.

In other words, when temperature increases, pressure increases.
When pressure decreases, temperature decreases.

Do you want to solve for:

I N S T R U C T I O N S

Similar to the calculations with Boyle's Law or Charles' Law, every word problem involving Gay-Lussac's Law will always give us 3 of the 4 variables. Of those 3 variables, we have to determine which two "pair up" (or which two were measured at the same time). To pair these correctly, these get designated as "P1" and "T1" or "P2" and "T2" but never as "P1" and "T2" or "P2" and "T1".

1) The temperature of a gas is 30 degrees Celsius and its pressure is 760 torr. If the temperature originally was 40°C, what was the original pressure?

The two variables that were measured at the same time (and can get "paired up") are 30°C (T₂) and 760 torr (P₂).
Yes, we could have classified these as T₁ and P₁ but either way, they are paired properly.
We are told that the original temperature was 40°C (T₁) and we must solve for the original pressure (P₁).
As it says at the top of this page, we always must use absolute temperature with this formula so we'll have to convert both temperatures to Kelvin.
T₁ = 40°C + 273.15 = 313.15 Kelvin T₂ = 30°C + 273.15 = 303.15 Kelvin

Solving Gay-Lussac's Law for P₁ we get:
P₁ = P₂ • T₁ ÷ T₂ P₁ = 760 torr • 313.15 K ÷ 303.15 K P₁ = 785.07 torr

Using the calculator, we click on the P1 button.
We then enter the 3 numbers 760 313.15 and 303.15 into the correct boxes then click "CALCULATE" and get our answer of 785.07 torr.

2) A gas has a temperature of 300 Kelvin and a pressure of 1.5 atmospheres. If the previous pressure was 1.2 atmospheres, what was the original temperature?

Pairing up and classifying the data we have T₂ = 300K P₂ = 1.5 atm P₁ = 1.2 atm and we must solve for T₁.
Solving Gay-Lussac's Law for T₁ we get:
T₁ = P₁ • T₂ ÷ P₂ T₁ = 1.2 atm • 300K ÷ 1.5 atm T₁ = 240K

Using the calculator, we click on the T1 button.
We then enter the 3 numbers in the correct boxes, then click "CALCULATE" and get our answer of 240K.

3) A gas with 2 atmospheres of pressure has a temperature of 250 Kelvin.
Calculate the pressure if the temperature increases to 300K.

The two items of data which "pair up" are 2 atmospheres (P₁) and 250 K (T₁).
The remaining data is the new temperature of 300K (T₂) and we must now solve for the fourth data item (P₂).
Solving Gay-Lussac's Law for (P₂) we get:
P₂ = P₁ • T₂ ÷ T₁ P₂ = 2 atm • 300 K ÷ 250 K P₂ = 2.4 atmospheres

Using the calculator, we click on the P2 button.
We then enter the 3 numbers into the correct boxes then click "CALCULATE" and get our answer of 2.4 atmospheres.

4) A gas at a temperature of 60° Fahrenheit has a pressure of .9 atmospheres. What is the new temperature if the pressure increases to 1.1 atm?

The two variables that were measured at the same time and which can get "paired up" are 60°F (T₁) and .9 atm (P₁).
Before we continue, we must convert that temperature to an absolute scale.
To change Fahrenheit to Rankine, we add 459.67 and so we get:
T₁ = 60°F + 459.67 = 519.67 Rankine.
P₂ is 1.1 atm and so we are ready to calculate T₂.
Solving Gay-Lussac's Law for T₂ we get:
T₂ = P₂ • T₁ ÷ P₁ T₂ = 1.1 atm • 519.67R ÷ .9 atm T₂ = 635.15R

Using the calculator, we click on the T2 button.
We then enter the 3 numbers into the correct boxes then click "CALCULATE" and get our answer of 635.15 Rankine.

The default setting is for 5 significant figures but you can change that by inputting another number in the box above.

Answers are displayed in scientific notation and for easier readability, numbers between .001 and 1,000 will be displayed in standard format (with the same number of significant figures.)
The answers should display properly but there are a few browsers that will show no output whatsoever. If so, enter a zero in the box above. This eliminates all formatting but it is better than seeing no output at all. _____________________

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