Chapter 15, Problem 44P

(a)

To determine

The efficiency of the heat engine to that of an ideal (Carnot) engine.

Answer to Problem 44P

The efficiency of heat engine to that of an ideal engine is $0.33$ .

Explanation of Solution

Given:

The given that heat reservoirs at $970\text{K}$ and $650\text{K}$ produces $550\text{J}$ of work per cycle for a heat input of $2200\text{J}$ .

Formula used:

Apply the efficiency formula to determine the efficiency of the heat engine.

Calculation:

The efficiency of the ideal engine is,

  $\begin{array}{l}{e}_i=1-\frac{T_i}{T_h}\\ e_i=1-\frac{650}{970}\\ e_i=0.33\end{array}$

Therefore, the efficiency of the heat engine to that of an ideal engine is $0.33$ .

(b)

To determine

The total entropy change of the universe per cycle of the real engine.

Answer to Problem 44P

The total entropy change of the universe per cycle of the real engine is $0.25$ .

Explanation of Solution

Given:

The given that heat reservoirs at $970\text{K}$ and $650\text{K}$ produces $550\text{J}$ of work per cycle for a heat input of $2200\text{J}$ .

Formula used:

Apply the efficiency formula to determine the efficiency of the actual engine

Calculation:

Calculate the efficiency of the actual engine

  $\begin{array}{l}{e}_a=\frac{W}{Q}\\ e_a=\frac{550}{2200}\\ e_a=0.25\end{array}$

Therefore, the total entropy change of the universe per cycle of the real engine is $0.25$ .

(c)

To determine

The total entropy change of the universe per cycle of a Carnot engine operating between the same two temperatures

Answer to Problem 44P

The total entropy change of the universe per cycle of a Carnot engine operating between the same two temperatures is $75.8\%$ .

Explanation of Solution

Given:

The given expression is that heat reservoirs at $970\text{K}$ and $650\text{K}$ produces $550\text{J}$ of work per cycle for a heat input of $2200\text{J}$ .

Formula used:

Apply the efficiency formula to determine the efficiency of the Carnot engine

Calculation:

Calculate the total entropy of the Carnot engine operating between the same two temperatures.

  $\begin{array}{l}{e}_c=\frac{e_a}{e_i}100\\ e_c=\frac{0.25}{0.33}100\\ e_c=75.8\%\end{array}$

Therefore, the total entropy change of the universe per cycle of a Carnot engine operating between the same two temperatures is $75.8\%$ .