Chapter U3.54, Problem 2E

Interpretation Introduction

Interpretation:

The method of calculating the volume of a gas at a certain temperature using the proportionality constant, k needs to be explained.

Concept Introduction :

The proportionalityconstant, k is given by $\text{k =}\frac{\text{y}}{\text{x}}$

where y and x are two quantities which are directly proportional. Once we find out the proportionality constant,we can find an equation and relationship between x and y, namely $\text{y = kx}$ .

Answer to Problem 2E

  $PV=k$

Explanation of Solution

The volume of a given mass of a gas is inversely related to pressure when the temperature is constant.

The relation is expressed by the below equation:

  $V\propto \frac{1}{P}$ means, Volume is inversely proportional to Pressure.

  $P\propto \frac{1}{V}$ means, Pressure is inversely proportional to Volume.

  $PV=k$ , or

  ${\text{P}}_{\text{1}}{\text{V}}_{\text{1}}{\text{= P}}_{\text{2}}{\text{V}}_{\text{2}}$

Where,

P = pressure

V = volume of a gas

k = constant in this equation

The above relation is known as Charles’s law.