Chapter 5, Problem 5.27P

Interpretation Introduction

Interpretation:

The final volume of a $93\text{ L}$ sample of dry air that is cooled from $145°\text{C}$ to $-22°\text{C}$ at constant pressure of $2.85\text{ atm}$ is to be calculated.

Concept introduction:

Chale’s law states that at constant pressure $\left(P\right)$ and when the amount of gas $\left(n\right)$ is fixed, the volume of gas is directly proportional to the absolute temperature $\left(T\right)$.

$V\propto T$ (1)

For two different values of volume and temperature equation (1) can be modified as follows:

$\frac{V_1}{T_1}=\frac{V_2}{T_2}$ (2)

Here,

$V_1$ is initial volume occupied by the gas molecules.

$V_2$ is the final volume occupied by the gas molecules.

$T_1$ is the initial temperature.

$T_2$ is the final temperature.

The conversion factor to convert $°\text{C}$ to Kelvin is as follows:

$T\left(\text{K}\right)=T\left(\text{°C}\right)+273.15$ (3)