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

Compressible Gas Flow - Entropy

Calculating the entropy in a compressible gas flow.

Sponsored Links

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

ds = cv ln(T2 / T1) + R ln(ρ1 / ρ2)                          (1)


ds = cp ln(T2 / T1) - R ln(p2 / p1)                            (2)


ds = change in entropy     (kJ)

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

cp = 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/m3)

p = absolute pressure      (Pa, N/m2)

Example - Entropy Change in an Air Heating Process

Air - 10 kg - is heated at constant volume from temperature 20 oC and 101325 N/m2 to a final pressure of 405300 N/m2.

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

p v = R T                   (3)


v = volume   (m3)

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

v1 = R T1 / p1                (4)

Since v1 = v2 the ideal gas equation (3) after heating can be expressed as:

p2 v1 = R T2                  (5)

or transformed to express the final temperature:

T2 = p2 v1 / R                (6)

Combining (5) and (6):

T2 = p2 (R T1 / p1) / R

    = p2 T1 / p1                  (7)

    = (405300 N/m2) (273 K + 20 K) / (101325 N/m2)

    = 1172 K - the final gas temperature

The change in entropy can be expressed by (2)

ds = cp ln(T2 / T1) - R ln(p2 / p1)

ds = (1.05 kJ/kgK) ln((1172 K) / (293 K)) - (0.33 kJ/kgK) ln((405300 N/m2) / (101325 N/m2))

        = 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

Sponsored Links

Engineering ToolBox - SketchUp Extension - Online 3D modeling!

3D Engineering ToolBox Extension to SketchUp - add parametric components to your SketchUp model

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 older versions of the amazing SketchUp Make and the newer "up to date" SketchUp Pro . Add the Engineering ToolBox extension to your SketchUp Make/Pro from the Extension Warehouse !

Translate this Page

Translate this page to Your Own Language .

About the Engineering ToolBox!

Privacy Policy

We don't collect information from our users. More about


This page can be cited as

  • The Engineering ToolBox (2004). Compressible Gas Flow - Entropy. [online] Available at: [Accessed Day Month Year].

Modify the access date according your visit.


3D Engineering ToolBox - draw and model technical applications! 2D Engineering ToolBox - create and share online diagram drawing templates! Engineering ToolBox Apps - mobile online and offline engineering applications!

Unit Converter


Sponsored Links