Chapter 14, Problem 51A

Interpretation Introduction

Interpretation: If a gas is compressed from 4L to 1 L at a constant temperature, the change in pressure needs to be explained.

Concept Introduction: According to Boyle’s law at a constant temperature, the volume of gas of a fixed number of moles is inversely proportional to its pressure.

This can be represented as follows:

  $P\propto \frac{1}{V}$

Thus, the relation between the initial and final pressure and volume of gas will be:

  $P_1{V}_1=P_2{V}_2$

Here, P is pressure and V is volume.

Explanation of Solution

At constant temperature, the relationship between the initial and final volume and pressure of the gas is as follows:

  $P_1{V}_1=P_2{V}_2$

Since, gas is compressed from 4 L to 1 L thus, the value of $V_1$ and $V_2$ is 4 L and 1 L respectively. Substitute the values,

  $P_1\left(4\text{ L}\right)=P_2\left(1\text{ L}\right)$

On rearranging,

  $P_1=\frac{P_2}{4}$

Or,

  $P_2=4P_1$

Therefore, the pressure becomes 4 times the initial value.