Chapter 15, Problem 51GP

To determine

The inventor claims to have designed and built an engine.

Explanation of Solution

Given information:

The given is $1.50\text{MW}$ of usable work while taking in $3.00\text{MW}$ of thermal energy at $425\text{K}$ , and rejecting $1.50\text{MW}$ of thermal energy at $215\text{K}$ .

Formula used:

The efficiency of thermal energy is given by,

  $e=\frac{W}{Q_H}$

  $e$ is a efficiency of engine, $W$ is a work done and $Q_H$ is the heat of engine.

Calculation:

Substitute the values in the formula,

  $\begin{array}{c}e=\frac{W}{Q_H}\\ =\frac{\frac{W}{t}}{\frac{Q_H}{t}}\\ =\frac{1.50\text{W}}{3.00\text{W}}\\ =0.500\end{array}$

  $\begin{array}{c}{e}_{\text{ideal}}=1-\frac{T_L}{T_H}\\ =1-\frac{215\text{K}}{425\text{K}}\\ =0.494\end{array}$

The efficiency is different.