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Chapter 21: Q. 17 (page 595)

A heat engine uses a diatomic gas in a Brayton cycle. What is the engine's thermal efficiency if the gas volume is halved during the adiabatic compression?

Short Answer

Expert verified

The engine's thermal efficiency during adiabatic compression,η=24%.

Step by step solution

01

Step: 1 Equating Adiabatic process equation:

Any thermal cycle's efficiency is expressed as

η=1−TcTh

We know that for an adiabatic process

pVγ=const

From the first law, we may express pressure in terms of temperature.

pV=nRT⇒p=nRTV∝TV−1

As a result, we have the following for an adiabatic process:

TVγ−1=const.

02

Step: 2 Equating:

Let us now calculate a temperature ratio based on the volume ratio:

TcVcγ−1=ThVhγ−1

We get that

TcTh=Vhγ−1Vcγ−1=VhVcγ−1.

03

Step: 3 Finding the value of Eficiency:

The Efficiency will be,

η=1−VhVcγ−1η=1−121.40−1=24%.

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Most popular questions from this chapter

A heat engine using 1.0molof a monatomic gas follows the cycle shown in FIGURE P21.55. 3750Jof heat energy is transferred to the gas during process 1→2.

a. Determine Ws,Q, and ΔEthfor each of the four processes in this cycle. Display your results in a table.

b. What is the thermal efficiency of this heat engine?

The coefficient of performance of a refrigerator is5.0. The compressor uses10Jof energy per cycle.

a. How much heat energy is exhausted per cycle

b. If the hot-reservoir temperature is27°C, what is the lowest possible temperature inC∘of the cold reservoir?

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A heat engine with a thermal efficiency of 40%does 100Jof work per cycle. How much heat is (a) extracted from the hot reservoir and (b) exhausted to the cold reservoir per cycle?

Consider a 1.0MW power plant (this is the useful output in the form of electric energy) that operates between 30oC and 450oC at 65% of the Carnot efficiency. This is enough electric energy for about 750 homes. One way to use energy more efficiently would be to use the 30oC“waste” energy to heat the homes rather than releasing that heat energy into the environment. This is called cogeneration, and it is used in some parts of Europe but rarely in the United States. The average home uses 70GJof energy per year for heating. For estimating purposes, assume that all the power plant’s exhaust energy can be transported to homes without loss and that home heating takes place at a steady rate for half a year each year. How many homes could be heated by the power plant?
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