Boyle's law

Introduction and Statement

Boyle's Law was stated by Robert Boyle in 1662. It describes the quantitative relationship between the pressure and volume of a gas at a constant temperature.

Statement: The volume of a given mass of a gas is inversely proportional to its pressure, provided the temperature remains constant.

Mathematical Formulation

According to Boyle's Law, when temperature $T$ and quantity of gas $n$ are kept constant:

$V \propto \frac{1}{P}$

Removing the proportionality sign:

$V = \frac{k}{P}$

Where $k$ is the proportionality constant. Rearranging the equation yields:

$P V = k$

This shows that the product of pressure and volume for a fixed mass of gas at constant temperature is always a constant value.

Initial and Final States

If a given mass of gas at initial pressure $P<em>1$ and initial volume $V</em>1$ undergoes a change to final pressure $P<em>2$ and final volume $V</em>2$ at constant temperature:

$P<em>1 V</em>1 = k$

$P<em>2 V</em>2 = k$

Equating both expressions gives:

$P<em>1 V</em>1 = P<em>2 V</em>2$

Experimental Verification

• Initial Condition: Consider a gas enclosed in a cylinder fitted with a movable piston. At pressure $P<em>1 = 2\,\text{atm}$, the volume of the gas is $V</em>1 = 2\,dm^3$. The product $P<em>1 V</em>1 = 2 \times 2 = 4\,\text{atm}\,dm^3$

• Final Condition: When the pressure is increased to $P<em>2 = 4\,\text{atm}$, the volume decreases to $V</em>2 = 1\,dm^3$. The product $P<em>2 V</em>2 = 4 \times 1 = 4\,\text{atm}\,dm^3$

• Conclusion: The product $P V$ remains constant, verifying Boyle's Law.

Graphical Representation

• Plotting pressure $P$ against volume $V$ at constant temperature yields a smooth curve called an isotherm.

• Plotting pressure $P$ against $\frac{1}{V}$ gives a straight line passing through the origin.