Chapter 4.8, Problem 32P

(A)

Interpretation Introduction

Interpretation:

The change in entropy of the universe

Concept Introduction:

Write the expression for entropy.

$dS=\frac{d{Q}_{rev}}{T}$

Here, the house temperature is $T$ and change in the reversible heat is $d{Q}_{rev}$.

Write the expression to calculate the change in entropy of the universe.

$\Delta S_{universe}=\Delta S_{system}+\Delta S_{surroundings}$

Here, entropy of the system is $\Delta S_{system}$ and entropy of the surrounding is $\Delta S_{surroundings}$.

(B)

Interpretation Introduction

Interpretation:

Is any heating system required to maintaining this house at $70°\text{F}$.

(C)

Interpretation Introduction

Interpretation:

The efficiency of Carnot heat engine and the net work done on the system.

Concept Introduction:

Write the expression to determine the efficiency of Carnot heat engine.

${\eta }_{\text{H}\text{.E}}=\left(1-\frac{T_C}{T_H}\right)\times 100\%$

Here, temperature of heat sink is $T_C$ and temperature of heat reservoir is $T_H$.

Write the efficiency of Carnot heat engine.

$\begin{array}{l}{\eta }_{\text{H}\text{.E}}=\frac{-W_{net}}{Q_{added}}\\ \left|W_{net}\right|={\eta }_{\text{H}\text{.E}}\times Q_{added}\end{array}$

Here, heat added to the system is $Q_{added}$ and net work done on the system is $W_{net}$.