Chapter 15, Problem 43P

To determine

The approximate net change in entropy of the system.

Answer to Problem 43P

The approximate net change in entropy of the system is $\approx 1.15\text{J/K}$ .

Explanation of Solution

Given information:

The given that $3.8\text{}\text{kg}$ piece of aluminum at ${30}^{\text{o}}\text{C}$ is placed in $1.0\text{kg}$ of water in a Styrofoam.

Formula used:

Apply the second law of thermodynamic to determine the change in entropy.

Calculation:

Calculate the equation,

  $\begin{array}{c}3.8\times 900\times T=1\times 4186\times \left(10-T\right)\\ 3420T=41860-4186T\\ 7606T=41860\\ T=5.503\end{array}$

Change in temperature in degrees Celsius

  $T={5.5}^{0}C$

Now, change the temperature in the into Kelvin,

  $\begin{array}{l}\frac{\left(4.5\times 1\times 4816\right)}{\left(293+4.5/2\right)}-\left(5.5\times 3.8\times 900\right)\left(303-5.5/2\right)\\ 63.800-62.648\approx 1.15\end{array}$

Therefore, the approximate net change in entropy of the system is $\approx 1.15\text{J/K}$ .