### Problem StatementA Carnot engine rejects 50% of the heat absorbed from a source to a sink at 27°C. What is the source temperature?### ExplanationThe problem describes a scenario involving a Carnot engine, which is a theoretical model of a thermodynamic engine used to explain the principles of thermodynamic cycles. The Carnot engine operates between a heat source and a heat sink, rejecting a certain percentage of heat absorbed from the source to the sink. In this problem, the heat sink is at 27°C.To solve this, we need to employ the Carnot efficiency formula and the relationship between the temperatures of the source and the sink.### Key Concepts1. **Carnot Efficiency**: The efficiency \(\eta\) of a Carnot engine is given by:\[ \eta = 1 - \frac{T_\text{sink}}{T_\text{source}} \]2. **Percentage of Heat Rejection**: If 50% of the heat is rejected, then \(\eta = 0.50\).3. **Temperature Conversion**: Temperatures must be converted to an absolute scale (Kelvin, K) for calculations:\[ T(K) = T(°C) + 273.15 \]### Steps to Solve:1. Convert the sink temperature to Kelvin: \[ T_\text{sink} = 27 + 273.15 = 300.15\,K \]2. Use the efficiency formula: \[ \eta = 1 - \frac{T_\text{sink}}{T_\text{source}} \]Since the Carnot engine rejects 50% of the heat, the efficiency \(\eta = 0.50\):\[ 0.50 = 1 - \frac{300.15}{T_\text{source}} \]3. Solve for \(T_\text{source}\): \[ \frac{300.15}{T_\text{source}} = 0.50 \] \[ T_\text{source} = \frac{300.15}{0.50} \] \[ T_\text{source} = 600.30\,K \] 4. Convert back to Celsius if required: \[ T_\text{source}(°C) = T_\text{source}(K) - 273.15 \] \[

Given data: TL=27°C=300 KQL=0.5QH Need to determine the source temperature.

Answered: A Carnot engine rejects 50% of the heat…

Engineering

Mechanical Engineering

A Carnot engine rejects 50% of the heat absorbed from a source to a sink at 27°C. What is the source temperature?

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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