Chapter 13, Problem 38P

To determine

To Find: The change in the configuration of the tire.

Answer to Problem 38P

  $7.4\%$

Explanation of Solution

Given:

  $T_1={\text{15}}^0\text{C}$

  $T_2={\text{38}}^0\text{C}$

Formula used:

Ideal gas equation:

  $\begin{array}{l}PV=nRT\\ \frac{PV}{R}=nT\\ n_1{T}_1=n_2{T}_2\\ \frac{n_2}{n_1}=\frac{T_2}{T_2}\end{array}$

Where,

P = pressure of the gas

V = Volume of the gas

T = temperature of the gas

n = number of moles.

Calculation:

  $\begin{array}{c}\frac{n_2}{n_1}=\frac{T_2}{T_2}\\ =\frac{\text{(273+15)K}}{\text{(273+38)K}}\\ =\frac{288}{311}\\ =0.926\\ =1-0.926\\ =0.074\\ 7.4\%\end{array}$

Conclusion:

The change in the configuration of the tire without a change in the pressure is $7.4\%$ .