How much heat transfer occurs to the environment per day by an electrical power station that uses 1.2 * 1014 J of heat transfer into the engine with an efficiency of 42%? How much electrical energy is generated per day?

Given: The total amount of heat transfer is 1.2×1014 J. The efficiency of the engine is 42%.…

Answered: How much heat transfer occurs to the…

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter21: Heat And The First Law Of Thermodynamics

Section: Chapter Questions

Problem 11PQ

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Question

How much heat transfer occurs to the environment per day by an electrical power station that uses 1.2 * 10¹⁴ J of heat transfer into the engine with an efficiency of 42%? How much electrical energy is generated per day?

Expert Solution

Step 1

Given:

The total amount of heat transfer is $1.2 \times 10^{14} J$ .

The efficiency of the engine is $42 %$ .

Introduction:

The efficiency of an engine is the ratio of the output to the input of the machines, the efficiency represents the amount of desired out has been obtained.

Step 2

Calculation:

The amount of heat transferred to the environment is the energy that has not been used.

Write the expression for the energy transferred to the environment.

$H_{e} = (1 - η) H_{t}$

Here, $H_{e}$ is the heat transferred to the environment, $η$ is the efficiency and $H_{t}$ is the total heat.

Substitute, $1.2 \times 10^{14} J$ for $H_{t}$ and $42 %$ for $η$ in the above expression.

$H_{e} = (1 - \frac{42}{100}) (1.2 \times 10^{14} J) H_{e} = 6.96 \times 10^{13} J$

Thus, the heat transferred to the environment is $6.96 \times 10^{13} J$ .

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