Lesson 2, Topic 3
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Boyle’s Law

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An English Physicist, Robert Boyle in 1962 studied the effect of pressure change on gas volume. His observations led to Boyle’s Law.

What is Boyle’s Law?

Boyle’s law states that the volume of a fixed mass of gas is inversely proportional to its pressure, provided temperature remains constant.

It means that at constant temperature, an increase in the pressure exerted on a fixed mass of gas leads to a decrease in the gas volume and vice versa.

Mathematically,

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

This proportionality can be converted into an equation by adding a constant, K.

i.e $$\scriptsize V = \normalsize \frac{1}{P}\scriptsize K$$

:- $$\scriptsize V = \normalsize \frac{K}{P}$$

Or PV = K

Where V = Volume

P = Pressure

K = Proportionality constant

Using the expression PV = K

For gas 1, we have P1V1 = K

For gas 2, we have P2V2 = K

Since K = K then,

P1V1 = P2V2 (at constant temperature)

Where P1 = Initial Pressure, P2 = Final Pressure

V1 = Initial Volume, V2 = Final volume

Boyle’s law can also be restated as the pressure of a given mass of gas inversely proportional to its volume, temperature remaining constant.

Graphical Representation of Boyle’s Law

The following can be obtained from the graphical representation of Boyle’s law.

(a) A plot of P against V is a curve, which is asymptotic with the x-and y-axis.

(b) A plot of V against 1/V (or v against 1/P) gives a straight line passing through the origin.

(c) A plot of PV against Pressure P (or volume V) is a straight horizontal line graph.

Pictorial Representation of Boyle’s Law

Figure above shows diagrammatically how kinetic theory of matter explains Boyle’s law which states that the volume of a gas is inversely proportional to its pressure.

How kinetic theory explains Boyle’s Law

A constant temperature, if the pressure on a given amount of gas is doubled, its volume will decrease by one-half. Conversely, if the pressure is decreased by one-half, the volume will double.

Calculations based on Boyle’s Law

1. A given mass of a gas occupies a volume of 300cm3 at 900mmHg pressure. Calculate the volume occupied by the same gas at 750mmHg if the temperature remains constant.

According to Boyle’s law

P1V1 = P2V2

P1 =900mmHg
VI = 300cm3
P2 = 750mmHg
V2 = ?

V2 = $$\frac{P_1 V_1}{P_2}\\ = \frac{900 \; \times \; 300}{750} \\ = \scriptsize 360cm^3$$

2. A certain mass of gas occupies 200cm3 at 1.0 x 105Nm-2, Calculate its volume when the pressure becomes 2.0 x 105 Nm-2 at constant temperature.

P1 = 1.0×105Nm-2
V1 = 200cm3
P2 = 2.0 X 105Nm-2
V2 = ?

V2 = $$\frac{P_1 V_1}{P_2}\\ = \frac{1.0 \; \times \; 10^5 \; \times \; 200}{2 \; \times \; 10^5} \\ = \scriptsize 100cm^3$$

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