Chapter 14, Problem 58A

Interpretation Introduction

Interpretation: The new temperature of the gas needs to be calculated if a gas of volume 15 L at $327{}^{\text{o}}\text{C}$ is cooled at constant pressure until the volume 5 L.

Concept Introduction: According to Charles’s law, at constant pressure, the volume of the gas is directly proportional to the temperature in K.

The mathematical relation is represented as follows:

  $\frac{V_1}{T_1}=\frac{V_2}{T_2}$

Here, V is volume and T is temperature.

Explanation of Solution

The volume of gas is 15 L at $327{}^{\text{o}}\text{C}$ . It is cooled to a volume of 5 L at constant pressure. The new temperature of the gas is calculated as follows:

  $\frac{V_1}{T_1}=\frac{V_2}{T_2}$

Or,

  $T_2=\frac{V_2\times T_1}{V_1}$

Here, the temperature must be in K; thus,

  $\begin{array}{c}T=\left(327+273\right)\text{ K}\\ =\text{600 K}\end{array}$

Substitute the values,

  $\begin{array}{c}{T}_2=\frac{\left(5\text{ L}\right)\left(\text{600 K}\right)}{\left(15\text{ L}\right)}\\ =200\text{ K}\end{array}$

Therefore, the new temperature of the gas is 200 K.