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Q. 18

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 595

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Short Answer

At what pressure ratio does a Brayton cycle using a monatomic gas have an efficiency of ?

The pressure ratio using a monatomic gas,

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Step by Step Solution

Step: 1 Definition of Brayton cycle:

The Brayton cycle is a thermodynamic cycle that works on the basis of constant pressure process . It involves four operation , like isentropic compression , constant pressure heat addition , isentropic expansion and constant pressure heat rejection. It is mostly used in gas turbine power plants.

Step: 2 Equating the Efficiency:

The performance of a Brayton engine operating at a compression ratio of r with a gas of heat capacity ratio of is calculated as follows:

Simplify as follows.

Therefore we have

Step: 3 Finding the value of :

The value of for air is 1.4 . Efficiency is 50% hence

The ratio is given by

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