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

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

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:

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Physics of Motion

Electrostatics

Electric Charge Field and Potential

Physical Quantities And Units

Fields in Physics

Dynamics

Study anywhere. Anytime. Across all devices.

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

Physics of Motion

Electrostatics

Electric Charge Field and Potential

Physical Quantities And Units

Fields in Physics

Dynamics

Study anywhere. Anytime. Across all devices.

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