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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 pressure (p₁)

Initial temperature (T₁)

Final pressure (p₂)

Final temperature (T₂)

Volume (V)

Amount of gas (n)

mol

Gas Constant (R)

J⋅K⁻¹⋅mol⁻¹

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An online free gay lussac’s law calculator assists you to get instant idea about gas parameters in an isochoric transformation.

Let’s discuss in detail the behaviour of gas heat and pressure while keeping the volume constant.

## Gay Lussac’s Law:

In the year 1802, a well-known chemist Sir Gay Lussac proposed a proper law about gas expansion.

#### Statement:

“For an ideal gas, the temperature of the gas is directly proportional to the pressure applied by gas molecules on the walls of the full-packed container”

This free gay-lussac’s law calculator also analyse such a behaviour of pressure and heat transitions in a span of moments.

### Gay Lussac’s Law Formula:

Mathematically, you can represent the temperature and pressure formula for Gay Lussac’s law as follows:

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

where;

$$P_{1}$$ = Initial Temperature

$$T_{1}$$ = Initial Temperature

$$T_{2}$$ = Final Temperature

$$P_{2}$$ = Final Pressure

Apart from this, you can also determine the moles of gas along with overall volume by using this ga-lussac’s law calculator.

Here if you want to study the pressure-volume relationship, you can also make use of another Boyle’s law calculator.

### Derivation of Gay Lussac’s Law:

Here we will see how to derive gay lussac’s law by using Charle’s and Boyle’s law expressions:

According to Boyle’s Law:

$$P_{1}*V_{1} = P_{2}*V \hspace{0.15in}…\left(1\right)$$

According to Charle’s Law:

$$T_{1}*V_{2} = T_{2}*V \hspace{0.15in}…\left(2\right)$$

You can also study the relationship among temperature and volume at constant pressure by using the free Charle’s law calculator

Comparing (1) and (2);

$$V = P_{1} × V_{1} × P_{2} \hspace{0.15in}…\left(3\right)$$

$$V = T_{1} × V_{2} × T_{2} \hspace{0.15in}…\left(4\right)$$

Comparing right sides of both above equations:

$$P_{1} × V_{1} × P_{2} = T_{1} × V_{2} × T_{2} = k$$

The above relation generates the following equation:

$$P*V = k*T$$

Which is the mathematical form of teh Gay lussac’s law formula and is also used by this online gay lussac’s law calculator.

### Real World Applications of Gay Lussac’s Law:

Let’s discuss about some real life examples of the law which are as under:

#### Firing:

What actually happens when you fire a bullet? Let us tell you! Just after the fire, the gunpowder creates a high pressure by a blast and thus allows the bullet to move with high speed up to longer distances. If you desire to estimate the actual pressure at the instant fire is done, you can use this free gay-lussac’s law calculator absolutely cost free.

#### Temperature Variation vs Tyre Pressure:

A tire acts like an enclosed container in which the pressure and temperature show a linear relationship. Whether it is hot or cold outside, the volume of the gas filled in it remains constant and temperature increase causes an increase in pressure and vice versa.

#### Air In The Balloon:

When you fill air in a balloon and keep it in a room with air conditioning on, the temperature decrease of air inside the balloon causes a considerable decrease in its pressure as well. This is a good example illustrating the gay lussac’s law calculator. Moreover, you can also justify the changes by using this free pressure and temperature calculator in a couple of seconds, without comprising the errors in calculations.

#### Heating An Aerosol Can:

When any aerosol just like those of a spray bottles are heard with the fire, the pressure increases inside. This is mainly due to the temperature pressure linear relation.

### How To Analyse Gas Parameters In Isochoric Medium?

Keeping the real gases away from the discussion, let’s resolve a couple of examples to clarify the concept of gay lussac’s law. Move on!

Example # 01:

How to find final pressure given initial pressure and temperature as per follows:

Initial temperature = 23K

Initial pressure = 12Pa

Final temperature = 4K

Solution:

Here we are going to use the gay lussac’s law equation as follows:

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

$$\frac{12}{23} = \frac{P_{2}}{4}$$

$$12P_{2} = 4*23$$

$$12P_{2} = 92$$

$$P_{2} = \frac{92}{12}$$

$$P_{2} = 7.66Pa$$

For full fledged and instant calculations, you can rely on the outputs generated by this free gay-lussac’s law formula calculator.

Example # 02:

A gas is enclosed in a container. After a certain warmth, the gas attains a temperature of about 34K along with the pressure being 9Pa. If the starting temperature was 23K, what would be the value of the Initial pressure?

Solution:

Using pressure and temperature formula below:

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

$$\frac{P_{1}}{23} = \frac{9}{34}$$

$$P_{1} = \frac{9*23}{34}$$

$$P_{1} = \frac{207}{34}$$

$$P_{1} = 6.08Pa$$

### How Gay Lussac’s Law Calculator Works?

Let’s go through the working guide of this pressure temperature calculator to understand how you could relate these two gas parameters in an isochoric media.

Input:

• Get going for selecting the parameter for the first list that you wish to calculate
• After you are done with your selection, now it’s time to enter all the required parameters
• Don’t forget to se;ect the unit against each element entered
• At last, it’s time to hit the calculate button

Output:

The free gay-lussac’s law calculator does the following computations:

• Estimates initial and final temperatures of the gas enclosed
• Likewise, the starting and final values of the pressures are also displayed upon selection
• Not only this, but the calculator also goes for determining the value of the gas volume and number of miles in a particular volume of the given gas

## FAQ’s:

### Why does temperature decrease with pressure?

No doubt there exists a direct relationship among temperature and pressure that could be estimated as well by using this gay-lussac’s law calculator. But when the temperature of the atmosphere is increased, the gas molecules are spread widely in the atmosphere which decreases the overall atmospheric pressure. This is why in such a situation, there comes an inverse relationship among both of these parameters.

### Does pressure increase with altitude?

Yes, it is true that the pressure of the atmosphere decreases with increasing height. It happens because of a couple of reasons. The first one is the density of the air molecules that decreases a lot. The second important factor is played by the gravitational force of the earth. At height the gravity on air molecules decreases. This causes the pressure to get low at altitudes. If you want to examine the pressure of the gas at different heights, you can blindly trust the calculations of this best pressure and temperature calculator.

### Why is pressure in the lower atmosphere high?

The most basic reason for high pressure in lower atmosphere is the variation in the heat. As we know that the earth is not uniformly heated by the sun at every corner. So the areas with low heights will be less warm and the pressure will be high in such areas. For any warm climatic region, you can determine the increase in the pressure by using this gay lussac’s law calculator in moments.

### Is high pressure hot or cold?

As the high pressure is maintained only when the air is cold enough and gas molecules are not broadly spread, that is why high pressure is cold enough. If you are also residing in the cold area, you can check the pressure increase by using our free gay lussac calculator.

### Is rain high or low pressure?

Of course low pressure. At low atmospheric pressure the water molecules become more dense and gravity on them increases enough than normal. That is why it rains at lower pressure.

## References:

From the source of Wikipedia: Gas laws, Boyle’s law, Charles’s law, Gay-Lussac’s law, Molar mass, Precision, Vapour density

From the source of Khan Academy: ideal gas law, molar form, Thermodynamics, Maxwell–Boltzmann distribution

From the source of Lumen Learning: Simple Gas Laws, Pressure and Temperature, Moles of Gas