# Combined Gas Law

In: Science

### Combined Gas Law

COMBINED GAS LAW SUMMARYThe combined gas law is a gas law which combines Charles's law, Boyle's law, and Gay-Lussac's law.

This law states: “The ratio between the pressure-volume product divided by the temperature of a system remains constant.”

This can be stated mathematically as:

￼

Where: p is the pressure, V is the volume, T is the temperature measured in kelvins, and k is a constant (with units of energy divided by temperature).

Reminder: 1atm= 760 torr = 101.3 kPa & Celsius to Kelvin= add 273 and Kelvin to Celsius= subtract 273

For comparing the same substance under two different sets of conditions, the law can be written as:

￼

If the problem does not state which unit to give the result in, then make sure that temperature is converted into Kelvin and for the Pressure and Volume just make sure you stay constant and use the same unit on both sides of the equation.

Combination of 3 Laws:

Boyle's Law states that the pressure-volume product is constant:

￼ In other words as external pressure on a gas increases the volume decreases, and vice versa.

Charles's Law shows that the volume is proportional to absolute temperature:

￼ In other words as temperature increases the volume increases, and vice versa.

Gay-Lussac's Law says that the pressure is proportional to the absolute temperature:

￼ In other words as temperature increases the pressure increases, and vice versa.

Where P is the pressure, V the volume and T the absolute temperature and of an ideal gas.

By combining (1) and either of (2) or (3) we can gain a new equation with P, V and T. Equation (2) is used in this example, and the subscript on the constant is dropped so that k = k2. ￼ We get the Combined Gas Law! (No specific scientist invented this law; rather three laws were just combined mathematically to come up with this law)

The combined gas law can be used to explain the mechanics where pressure, temperature, and volume are affected. For example: air conditioners, refrigerators...