Chapter 10, Problem 109RQ

Interpretation Introduction

Interpretation:

The pressure in the tire of an automobile on a hot day in Death Valley at a given temperature is to be calculated.

Concept Introduction:

Gay-Lussac’s law explains the variation between the pressure and temperature of a gas at a constant volume and amount of that gas. It states that the pressure of the gas $\left(P\right)$ is proportional to its temperature $\left(T\right)$. Mathematically, it is expressed as:

$P\alpha T$

The pressure $\left(P\right)$ of a body is calculated by dividing the force $\left(F\right)$ applied to that body with the area $\left(A\right)$ of the displaced body due to the applied force. Mathematically, the expression is:

$P=\frac{F}{A}$.

The conversion of the temperature value from Fahrenheit to Celsius has taken place using the conversion factor:

$t_{\text{F}}=\left(\frac{9°\text{F}}{5°\text{C}}\right)t_{\text{C}}+32°\text{F}$

Here $t_{\text{F}}$ is the temperature at Fahrenheit and $t_{\text{C}}$ is the temperature at Celsius.

Conversion of the given temperature values from Celsius to Kelvin is done by using the relationship:

$\text{K}=273.15+°\text{C}$