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.

• the most efficient way to navigate the Engineering ToolBox!

# Compressible Gas Flow - Entropy

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)

## 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.

## 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!