Gay Lussac's Law Calculator

When there is a constant amount of gas in a closed and rigid container, Gay-law Lussac's states the relationship between pressure and temperature. The gas container must be built in such a way that the volume of the gas remains constant under any condition for Gay-law Lussac's to hold. To put it another way, Gay-law Lussac's describes how an ideal gas behaves throughout an isochoric (constant-volume) process.

Gay Lussac's Law Formula & Derivation

Pressure law is another name for Gay Lussac's law. The absolute pressure is directly proportional to the temperature, according to this law. When a constant amount of gas is contained in a closed and rigid vessel, Gay Lussac's law is used to determine the relationship between pressure and temperature, as long as the volume of gas remains constant. The following equation describes the link between pressure and temperature.

Pf/Tf = Pi/Ti

Where Pi and Ti are the starting pressure and temperature and Pf and Tf are the final pressure and temperature readings.

One variation of the Gay-law Lussac's formula can be expressed as follows, using the definition above i.e. P₁/T₁ = P₂/T₂. Where Where P₁ is the initial pressure and T₁ is the starting temperature. Similarly, the final values of these gas parameters are P₂ and T₂.

This isn't the only way to look at the problem. If you wanted to check the relationship between the starting and end pressures, for example, you could use the formula T₁/T₂ = P₁/P₂. As can be seen, the initial and final temperature ratios are proportional to the initial and final pressure ratios

If you know the other three, you can evaluate any of these four parameters using this Gay-law Lussac's calculator. Simply enter the three known values, and the fourth will be calculated automatically. Furthermore, you may calculate the amount of gas in moles in an advanced mode based on the container's volume.

The procedures for using the calculator based on Gay Lussac's Law to find the unknown quantity are given here.

• Fill in the input fields with the specified values, such as Pi, Ti, and Tf
• Write x for the unknown quantity. Let's say Pf=x
• To receive the result, click the "Calculate x" button

Example 1:

Let's pretend we're in a 20°C room with a metal can containing 300 ml of air, and the gas's starting pressure is 100 kPa (or 105 Pa in scientific notation). Then we heat our container till it reaches a temperature of 400°C. What is the final value of the pressure within the container, assuming it isn't leaking?

Solution:

To begin, we first convert the temperatures into Kelvin, the absolute scale required by Gay-law: Lussac's

• T1 = 20°C = 293.15 K,
• T2 = 400°C = 673.15 K.
• T1 = 20°C = 293.15 K.
• T2 = 400°C = 673.15 K

To estimate the final pressure, rearrange Gay-law Lussac's formula i.e. P₂ = P₁ / T₁*T₂ = = 100 kPa / 293.15 K * 673.15 K = 229.63 kPa

Using the information supplied in the question, we can calculate the amount of gas in moles i.e. n = p1 * V1 / (R * T1) = 100 kPa * 300 ml / (8.314 J/(mol*K) * 293.15 K) = 0.0123 mol

Example 2:

We have a rigid box filled with nitrogen in this case, and we know it is heated to 460 K with an internal pressure of 1.6 atm. It is cooled to the point where the pressure decreases to 1 atm after some time. What's the final temperature going to be?

Solution:

Rearranging the Gay Lussacs Law Formula to find the unknown we have T₂ = T₁*P₂/P₁

= 460 K * 1 atm / 1.6 atm = 287.5 K

See how Gay-law Lussac's operates in our daily lives by considering the following examples

• Seasonal Variations in Tyre Pressure: Have you ever pumped a tyre in the winter only to find that it was over inflated as the weather warmed up? Or, conversely, did the pressure drop when it cooled down when it was filled over the summer? Tires are a closed system in this scenario, thus the higher the thermal, the higher the pressure.
• A saucepan's lid: It may appear obvious at first, but why does the cover jump and rattle around while you're boiling your food in a pot? As the temperature rises, the pressure of the gas inside the saucepan rises as well. When the pressure is strong enough to lift the lid and discharge the surplus gas, the pressure is released.
• Pouring hot water into a chilly container: If you don't believe us, this is a simple approach to see if Gay-law Lussac's is correct. Simply heat up an empty metal can of your favourite beverage in a safe manner. We strongly advise you to do this outside, rather than at home! After a short period, try plugging the hole and submerging the can in cold water. If you succeed, the can will shrink as the interior temperature drops, causing the pressure within to reduce as well.

1. What limitations apply to the use of Gay-law Lussac's of merging volumes?

It only applies to gases that have been measured at the same temperature and pressure. What is the relationship between the volume of a gas and the number of molecules present at the same temperature and pressure.

2. When the temperature of a closed gaseous system doubles, what happens to the pressure?

When the temperature of a closed gaseous system doubles, what happens to the pressure? This law illustrates that temperature and pressure have a direct relationship: as temperature rises, pressure rises correspondingly. The second temperature is equal to the first temperature multiplied by two.

3. What is the formula of Gay Lussac's Law?

The formula of Gay Lussac's Law is given by P₁/T₁ = P₂/T₂