Chapter 21: Q. 18 (page 595)

At what pressure ratio does a Brayton cycle using a monatomic gas have an efficiency of $50 %$ ?

Short Answer

Expert verified

The pressure ratio using a monatomic gas, $r = 11.3 .$

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 $γ$ is calculated as follows:

$\begin{aligned} η = 1 - \frac{1}{r^{\frac{γ - 1}{γ}}} \end{aligned}$
Simplify as follows.

$\begin{aligned} \frac{1}{r^{\frac{γ - 1}{γ}}} = 1 - η \end{aligned}$

Therefore we have

$r^{\frac{γ - 1}{γ}} = \frac{1}{1 - η} .$

Step: 3 Finding the value of r:

The value of $γ$ for air is 1.4 . Efficiency is 50% hence $η = . 50$

The ratio $r$ is given by

localid="1649322326172" $\begin{aligned} r = \sqrt[\frac{γ - 1}{γ}]{\frac{1}{1 - η}} \\ r = \sqrt[\frac{1.40 - 1}{1.40}]{\frac{1}{1 - 0.5}} = 11.3 . \end{aligned}$

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At what pressure ratio does a Brayton cycle using a monatomic gas have an efficiency of $50 %$ ?

Short Answer

Step by step solution

Step: 1 Definition of Brayton cycle:

Step: 2 Equating the Efficiency:

Step: 3 Finding the value of r:

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At what pressure ratio does a Brayton cycle using a monatomic gas have an efficiency of50% ?

Short Answer

Step by step solution

Step: 1 Definition of Brayton cycle:

Step: 2 Equating the Efficiency:

Step: 3 Finding the value of r:

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Work Energy and Power

Electricity and Magnetism

Wave Optics

Modern Physics

Radiation

Astrophysics

Study anywhere. Anytime. Across all devices.

At what pressure ratio does a Brayton cycle using a monatomic gas have an efficiency of $50 %$ ?