Chapter U3.54, Problem 1E

Interpretation Introduction

Interpretation:

The proportionality constant, k for a sample of gas, needs to be explained.

Concept Introduction :

The proportionality constant, 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 proportionalityconstant,we can find an equation and relationship between x and y, namely $\text{y = kx}$ .

Answer to Problem 1E

k is calculated by $\text{k =}\frac{\text{y}}{\text{x}}$

Explanation of Solution

At constant pressure for a gaseous sample, the ratio of volume of gas to its Kelvin temperature is constant.

i.e. $\frac{\text{V}}{\text{T}}\text{ = k}$ , a proportionality constant

This is known as Charles' Law.

Now, to determine this proportionality constant for a particular gas sample, we can take a Temperature and measure the volume that the gas sample occupies for that temperature. If T1 is the temperature and V1 is the Volume of gas,

  $\text{k = }\frac{\text{V1}}{\text{T1}}$

We can determine the value of k for a sample of gas by this method.