Chapter 15, Problem 56GP

To determine

The change in the entropy of the universe.

Answer to Problem 56GP

The change in the entropy of the universe is $2614.59\text{J/K}$ .

Explanation of Solution

Given info:

The mass of the cars is, $m=1100\text{kg}$ .

*The speed of the car is: $v=95\text{km}/\text{h}=\left(95\text{km}/\text{h}\right)\left(\frac{1000\text{m}}{1\text{km}}\times \frac{1\text{h}}{3600\text{s}}\right)=26.39\text{m}/\text{s}$ .

*The temperature of the surrounding is: $T=20°\text{C}=\left(20°\text{C}+273\right)\text{K}=293\text{K}$ .

Formula Used:

The expression to calculate the change in the entropy of the universe is,

  $\begin{array}{c}S=\frac{2\left(0.5m{v}^2\right)}{T}\\ S=\frac{m{v}^2}{T}\end{array}$

Calculation:

Substitute all the values in the above expression.

  $\begin{array}{c}S=\frac{\left(1100\text{kg}\right){\left(26.39\text{m}/\text{s}\right)}^2}{293\text{K}}\\ =2614.59\text{J/K}\end{array}$

Conclusion:

Thus, the change in the entropy of the universe is $2614.59\text{J/K}$ .