Chapter 14, Problem 95A

Interpretation Introduction

Interpretation: The reason for graphs for the three samples to not be identical needs to be explained.

Concept Introduction: Ideal gas equation is represented as follows:

  $PV=nRT$

Here, P is pressure, V is volume, n is number of moles, R is Universal gas constant and T is temperature.

Explanation of Solution

A gas can be described by variables such as number of moles, pressure, volume and temperature. Now, the given graph shows the relationship between volume and temperature of three different gas samples. It can be seen that the graph is not identical for all the three gasses.

Use ideal gas equation to understand the relation between volume and temperature of a gas.

  $PV=nRT$

This can be rearranged as follows:

  $V=\frac{nRT}{P}$

Here, graph between V and T is a straight line as above formula follow the straight line equation.

The equation for a straight line is as follows:

  $y=mx+c$

On comparing, the intercept of graph is 0 and slope is $\frac{nR}{P}$ .

It can be seen from the graph that three straight lines for three gases have different slopes.

Now, R is gas constant thus, it is same for all the three gases but pressure is a variable. Thus, three gas samples have different graphs due to different pressure values.