Two Carnot heat engines operate between the heat reservoirsas shown. If one engine has triple efficiency than another,determine the temperature TH*.

Answered: Two Carnot heat engines operate between…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

Two Carnot heat engines operate between the heat reservoirs
as shown. If one engine has triple efficiency than another,
determine the temperature TH*.

Expert Solution

Step 1

The thermal efficiency for left side Carnot heat engine is written as,

$\begin{array}{rcl} η_{t h} & = & \frac{T_{m a x} - T_{m i n}}{T_{m a x}} \\ = & \frac{T_{H} - T_{L}}{T_{H}} \\ η_{t h} & = & 1 - \frac{T_{L}}{T_{H}} . . . . . . (1) \end{array}$

The efficiency for right side Carnot heat engine is written as,

$\begin{array}{rcl} 3 η_{t h} & = & \frac{T_{m a x} - T_{m i n}}{T_{m a x}} \\ = & \frac{T_{H *} - T_{L}}{T_{H *}} \\ η_{t h} & = & \frac{1}{3} (1 - \frac{T_{L}}{T_{H *}}) . . . . . . (2) \end{array}$

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