Search the World of Chemistry

×

The Equation of Gay-Lussac's Law

18th Dec 2019 @ 3 min read

Physical Chemistry

The Equation of Gay-Lussac's law is P = kT. Here, P and T are the pressure and temperature of an enclosed ideal gas and k is a constant of proportionality.

Gay-Lussac's law says the pressure of an enclosed ideal gas is directly proportional to its temperature at the constant volume of the gas. The law is sometimes called pressure law because it relates the pressure of a gas to the temperature of the gas.

For a fixed amount of gas at the constant volume, the pressure P is directly proportional to the temperature T.

Pressure is proportional to temperature.

Removing the proportionality,

P=kT

Here, k is a constant of proportionality.

Rearranging the equation,

Gay-Lussac's law equation

From the above expression, the ratio of pressure to temperature (PV) remains constant when the volume (V) and the amount (n) of gas are constant.

Note: In the above expression, the temperature is in an absolute scale (kelvin).

The equation of Gay-Lussac's law in the celsius scale

Let T and t be the temperature in the kelvin and the degree celsius.

The relation between temperature in kelvin to the temperature in the degree celsius

Substituting T,

The formula after substituting T Gay-Lussac's equation in the degree celsius

Here, k1 = k × 273.15. The above equation is a straight similar to y = mx + c.

Gay-Lussac's law under different conditions

Let P1 and P2 be pressures at temperatures T1 and T2 respectively. We can establish the relation between the two conditions.

Pressure and temperature at two different conditions
Pressure and temperature at two different conditions

For an enclosed ideal gas at the constant volume,

Pressure to temperature ratio at two conditions

Combining both equations,

Gay-Lussac's law formula

From the above formula, we can calculate the pressure or the temperature at any unknown condition if the pressure and the temperature are known at any one condition.

Let take an example to better understand it.

Example 1

Statement: A cruise ship voyages from the port of San Diego to the port of Seattle. The ship is equipped with carbon dioxide (CO2) cylinders for fire safety. The temperature and pressure of the cylinder gas at San Diego is 12 °C and 50.1 bar. What will the pressure of the gas when the ship arrives at Seattle? The temperature at Seattle will be 5 °C when the ship arrives.

Temperature at San Diego and Seattle
Temperature at San Diego and Seattle

Solution: Let T1 and T2 be the temperatures at San Diego and Seattle.

Temperature at San Diego Temperature at Seattle

Let P1 and P2 be the pressures at San Diego and Seattle. P1 = 50.1 bar.

From Gay-Lussac's law,

The ratio of pressure to temperature at both conditions The pressure at Seattle

Thus, the pressure at Seattle is 48.9 bar.

The pressure at San Diego and Seattle
The temperature and pressure at San Diego and Seattle

When the temperature of the gas decreases from 12 °C to 5 °C, the pressure also decreases from 50.1 bar to 48.9 bar. This explains Gay-Lussac's law.

We can generalize the equation to any number of conditions. Consider a fixed amount of gas of the volume V. Let (P1, T1), (P2, T2), (P3, T3)… (Pi, Ti) be pressure and temperature at different conditions.

Pressure and temperature at i conditions
Pressure and temperature at i different conditions

According to the law, the ratio of pressure to temperature remains constant.

Gay-Lussac's formula for and different conditions

Example 2

Statement: Let us continue with the above example. The ship after reaching the port of Seattle is scheduled to travel towards the port of Anchorage, Alaska. Find the pressure of the gas in Anchorage if the temperature is −7 °C?

The temperature at San Diego, Seattle, and Anchorage
The temperature at San Diego, Seattle, and Anchorage

Solution: Let T3 be the temperature of the gas at Anchorage.

The temperature at Anchorage

The pressure P3 at Anchorage is

The pressure at Anchorage

Thus, the pressure at Anchorage is 46.8 bar.

The pressure at Anchorage
The temperature and pressure at San Diego, Seattle, and Anchorage

Associated articles

If you appreciate our work, consider supporting us on ❤️ patreon.
Gay Lussac Law Gas Law

Copy Article Cite

Thanks for your response!
Write a response


Join the Newsletter

Subscribe to get latest content in your inbox.

newsletter

We won’t send you spam.