Chapter 15, Problem 41P

To determine

The rate entropy increases per unit time.

Answer to Problem 41P

The rate entropy increases per unit time is $4.346\times {10}^{-2}\text{J/s}$ .

Explanation of Solution

Given information:

Rate of conduction, $\frac{Q}{t}=7.50\text{cal/s}$

Temperature of heat source, $T_{\text{s}}=240°\text{C}=240+273=513\text{K}$

Temperature of water, $T_{\text{w}}=27°\text{C}=27+273=300\text{K}$

Formula used:

Write the expression to calculate the rate of change of entropy per unit time.

  $\frac{{\left(\Delta s\right)}_{\text{Total}}}{t}=\frac{{\left(\Delta s\right)}_{\text{s}}}{t}+\frac{{\left(\Delta s\right)}_{\text{w}}}{t}$.......... (1)

Calculation:

Consider the conversion factor to convert rate of conduction from $\text{cal/s}$ to $\text{J/s}$ .

  $\begin{array}{c}7.50\text{cal/s}=7.50\times 4.18\text{J/s}\\ =31.4\text{J/s}\end{array}$

Since, the heat is transferred from source to water. Therefore, the rate of change of entropy of source is negative.

Substitute the values in equation (1).

  $\begin{array}{c}\frac{{\left(\Delta s\right)}_{\text{Total}}}{t}=-\frac{\left(31.4\right)}{513}+\frac{\left(31.4\right)}{300}\\ =-0.06120+0.10466\\ =4.346\times {10}^{-2}\text{J/s}\end{array}$

Therefore, therate entropy increases per unit time is $4.346\times {10}^{-2}\text{J/s}$ .