The Combined Gas Law is the law that combines three more gas laws, Charles’s law, Gay-Lussac’s law, and Boyle’s law. Three previously discovered laws have been combined to create this law. This law relates one thermodynamic variable to another while holding all other variables constant. The interdependence of these variables is illustrated by the combined gas law, according to which the ratio between pressure volume and temperature is constant.

Moreover, the ratio of volume and pressure and the gas’s absolute temperature should be constant in this law. It should be noted that when Avogadro’s law happens to combined gas law, then gas law shows results. Combined gas has been discovered like that only. Hence, It is simply a combination of other gas laws.

## Understanding Combined Gas Law

In order to understand the combined gas law, first, it is important to understand are previous other three discovered laws. so, let’s look into this-

### Boyle’s law

Let’s take an example, If a diver were to begin diving with full lungs, his lungs would be full of air. The pressure in his lungs also increases as he dives deeper underwater.

The lungs become squished when the pressure increases. Thus, the volume is reduced. Boyle’s law says that higher pressure equates to a lower volume, so in this case, pressure means lower volume. This is called Boyle’s Law. And the formula for Boyle’s law is PV=K.

Hence, Boyle’s Law states that the Higher the pressure (P), the lower the volume (V).

### Charles’s law

Let’s understand with the help of an example, that currently, there is a balloon in the refrigerator. The gas volume inside the balloon decreases as the temperature of the balloon in the refrigerator decreases.

Additionally, the balloon will revert to its original size once it is out. So, when the temperature increases, the volume increases as well. This is a manifestation of Charles’ Law. And the formula for Charles’s law is V/T=K.

Hence, Charles’s law states that the higher the temperature (T), the higher the volume (V).

### Gay-Lussac’s law

Assume that a driver is driving a car and gradually, the temperature inside the tire started increasing. So, as a result of which the air inside the tire will expand the tire, and consequently pressure inside the tire will increase. This is the Law of Gay-Lussac. And the formula for Gay-Lussac’s law is P/T=K.

Hence, Gay-Lussac’s law shows the relationship between temperature (T) and Pressure (P) keeping volume (V) constant (K). which shows that as the temperature (T) increases, the consequent pressure (P) also increases.

After combing Boyle’s law, Charles’s law, and Gay-Lussac’s law together, we form the combined Gas Law, which further shows that:

- Pressure is inversely proportional to volume, or higher volume equals lower pressure.
- Pressure is directly proportional to temperature, or higher temperature equals higher pressure.
- Volume is directly proportional to temperature, or higher temperature equals higher volume.

### Derivation of Combined Gas Law

As we have already discussed the Combined Gas Law is the amalgamation of the above three laws. The derivation of the combined gas law is like this:

Boyle’s law- PV=K, Charles’s law- V/T=K, and Gay-Lussac’s law- P/T=K.

So, the formula for combined gas law is PV/T = K. where P is pressure, V is volume, T is temperature, and K is constant. It is important to keep in mind that temperature must always be calculated in Kelvin. And, if units are available in celsius then first it must be converted into Kelvin by adding 273 to the particular unit.

Likewise, when two substances are compared or calculated in two different conditions, then the formula can be –

P1V1/T1 = P2V2/T2

Further, we will discuss how the application of these formulae is done in the solved examples.

### Solved Examples

**Example 1**

The initial volume of the gas is 5L and the final volume is 3L Calculate the final pressure of the gas, given that the initial temperature is 273 K, the final temperature is 200 K, and the initial pressure is 25 kPa.

**Solution**

According to the given parameters,

P1= 25 kPa, V1 = 5L, V2 = 3L, T1 = 273K, T2_{ }= 200K

According to combined gas law,

P1V1/T1 = P2V2/T2

Substituting in the formula, we get

25 x 5 / 273 = P2_{ }x 3 / 200

Therefore, P2 = 30.525 kPa

**Example 2**

Determine the volume of a gas given V1 = 3L, T1 = 300K, T2 = 250K, P1 = 35 kPa and P2= 50 kPa

**Solution**

Given Parameters are

P1 = 35 kPa, V1 = 3L, T1 = 300K, P2= 50 kPa, T2 = 250K

According to given parameters, we have an equation

P1V1/T1 = P2V2/T2

Substituting in the above equation, we get

35 x 3 / 300 = 50 x V2 / 250

Therefore, V2 = 1.75 L