Engineering ToolBox - Resources, Tools and Basic Information for Engineering and Design of Technical Applications!

This is an AMP page - Open full page! for all features.

Compressible Gas Flow - Entropy

Sponsored Links

The entropy change in a compressible gas flow can be expressed as

ds = c v ln(T 2 / T 1 ) + R ln(ρ 1 / ρ 2 ) (1)

or

ds = c p ln(T 2 / T 1 ) - R ln(p 2 / p 1 ) (2)

where

ds = change in entropy (kJ)

c v = specific heat capacity at a constant volume process (kJ/kgK)

c p = specific heat capacity at a constant pressure process (kJ/kgK)

T = absolute temperature (K)

R = individual gas constant (kJ/kgK)

ρ = density of gas (kg/m 3 )

p = absolute pressure (Pa, N/m 2 )

Example - Entropy Change in an Air Heating Process

Air - 10 kg - is heated at constant volume from temperature 20 o C and 101325 N/m 2 to a final pressure of 405300 N/m 2 .

The final temperature in the heated air can be calculated with the ideal gas equation :

p v = R T (3)

where

v = volume   (m 3 )

The ideal gas equation (3) can be transformed to express the volume before heating:

v 1 = R T 1 / p 1 (4)

Since v 1 = v 2 the ideal gas equation (3) after heating can be expressed as:

p 2 v 1 = R T 2 (5)

or transformed to express the final temperature:

T 2 = p 2 v 1 / R (6)

Combining (5) and (6):

T 2 = p 2 (R T 1 / p 1 ) / R

= p 2 T 1 / p 1 (7)

= (405300 N/m 2 ) (273 K + 20 K) / (101325 N/m 2 )

= 1172 K - the final gas temperature

The change in entropy can be expressed by (2)

ds = c p ln(T 2 / T 1 ) - R ln(p 2 / p 1 )

ds = (1.05 kJ/kgK) ln((1172 K) / (293 K)) - (0.33 kJ/kgK) ln((405300 N/m 2 ) / (101325 N/m 2 ))

= 1 (kJ/kgK)

Total change in entropy:

dS = (1 kJ/kgK) (10 kg)

= 10 (kJ/K)

Sponsored Links

Related Topics

Fluid Mechanics

The study of fluids - liquids and gases. Involving velocity, pressure, density and temperature as functions of space and time.

Related Documents

2nd Law of Thermodynamics

Entropy and disorder.

Steam Entropy

Basic steam thermodynamics - entropy diagram.

Superheated Steam - Entropy

The entropy of steam superheated to temperatures above saturation points.

Wet Bulb Globe Temperature (WBGT)

The Wet Bulb Globe Temperature can be used to measure the general Heat-Stress index.

Sponsored Links

Search Engineering ToolBox

  • the most efficient way to navigate the Engineering ToolBox!

SketchUp Extension - Online 3D modeling!

Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your Sketchup model with the Engineering ToolBox - SketchUp Extension - enabled for use with the amazing, fun and free SketchUp Make and SketchUp Pro . Add the Engineering ToolBox extension to your SketchUp from the Sketchup Extension Warehouse!

Privacy

We don't collect information from our users. Only emails and answers are saved in our archive. Cookies are only used in the browser to improve user experience.

Some of our calculators and applications let you save application data to your local computer. These applications will - due to browser restrictions - send data between your browser and our server. We don't save this data.

Google use cookies for serving our ads and handling visitor statistics. Please read Google Privacy & Terms for more information about how you can control adserving and the information collected.

AddThis use cookies for handling links to social media. Please read AddThis Privacy for more information.