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Chapter 21: Q 3 (page 593)

Could you have a heat engine with $η > 1$ ? Explain.

Short Answer

Expert verified

A heat engine with $n > 1$ is No.

Step by step solution

01

Step :1 Introduction

A heat engine is a machine that turns heat into mechanical energy. It receives heat from a reservoir, then performs some work, such as moving a piston or raising a weight, before releasing heat energy into the sink.

02

Step ;2 Explanation

Let us derive an expression for the efficiency of a heat engine. We can define heat engine efficiency as:

$\begin{aligned} η \end{aligned}$ $= W Q_{1}$

W

= Work done by the engine

$Q_{1}$

= Heat taken from the source

03

Step :3 Substitution

$Since η = W_{out} / Q_{in} and W_{out} < Q_{in} always, hence η < 1 always.$

No

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Most popular questions from this chapter

In Problems $65$ through $68$ you are given the equation(s) used to solve a problem. For each of these, you are to

a. Write a realistic problem for which this is the correct equation(s).

b. Finish the solution of the problem.

$0.20 = 1 - Q_{C} / Q_{H}$

$W_{out} = Q_{H} - Q_{C} = 20 J$

A heat engine satisfies $W_{o u t} = Q_{o u t}$ Why is there no $Δ E_{th}$ term in this relationship?

What are (a) $W_{out}$ and $Q_{H}$ and (b) the thermal efficiency for the heat engine shown in $FIGURE EX 21.14 ?$

Engineers testing the efficiency of an electric generator gradually vary the temperature of the hot steam used to power it while leaving the temperature of the cooling water at a constant $20 ° C$ . They find that the generator’s efficiency increases at a rate $3.5 \times 10^{- 4} K^{- 1}$ at steam temperatures near $300 ° C$ . What is the ratio of the generator’s efficiency to the efficiency of a Carnot engine?

Which, if any, of the heat engines in FIGURE EX 21.22 violate (a) the first law of thermodynamics or (b) the second law of thermodynamics? Explain.

See all solutions

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