# Gas Laws Revision Notes

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13.9Gas Laws

In these revision notes for Gas Laws, we cover the following key points:

• What is the relationship between pressure and volume of an ideal gas at constant temperature?
• What is the relationship between pressure and temperature of an ideal gas at constant volume?
• What is the relationship between volume and temperature of an ideal gas at constant pressure?
• What is the relationship between volume and amount of an ideal gas at constant temperature and pressure?
• What does the P - V graph represent in each case?

## Gas Laws Revision Notes

A process in which the temperature remains constant during the entire event (T1 = T2 = T) is known as isothermal process. The relationship between pressure and volume at constant temperature is known as the Boyle's Law and mathematically it is written as

P1 × V1 = P2 × V2

where the index 1 means "initial state" and 2 means "final state."

The P - V graph of an isothermal process is a hyperbola as pressure and volume vary inversely to each other.

A thermal process in which the volume remains constant (V1 = V2 = V) is known as isovolumetric (isohoric) process. The relationship between pressure and temperature at constant volume is given by the equation

P1/P2 = T1/T2

The above equation is known as the Gay-Lussac's Law.

The P - V graph for an isovolumetric process is a vertical line.

Any thermal process, which occurs at constant pressure is known as isobaric process. We write P1 = P2 = P. The relationship between volume and temperature at constant pressure is given by the equation

V1/V2 = T1/T2

The above equation is known as the Charles's Law.

The area under the P - V graph at constant pressure represents the work done by the gas during the expansion (or the work done on the gas during the contraction).

Any additional amount of gas (which means an extra number of molecules) simply brings an increase in volume of gas when no change in the other parameters occur. This phenomenon was first explained by Avogadro, so the relationship between the volume of ideal gas and the number of its molecules is known as the Avogadro's Law. Its mathematical expression is

V1/V2 = n1/n2

where n is the number of moles.

Avogadro's Law is intended for ideal gases but it is valid for real gases if the values of pressure and temperature are low.

From experiment, it has been found that one mole of an ideal gas occupies 22.4 L of volume at normal temperature and standard atmospheric conditions.

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