# Air Compressors

Examines the application of the gas laws to Air Compressors and Motors.

**Contents**

## Introduction

Single Stage Reciprocating without Clearance: Stage 1 - a- Suction Stroke: The inlet valve opens and the cylinder fills with air at Ambient Pressure.

- Compression Stroke: Both Valves are shut. The Pressure is raised from to .

- Delivery Stage: The Exhaust Valve opens. Air at is delivered to the receiver at Constant Pressure.

### For Reciprocating Compressors:

- The efficiency referred to is the Isothermal case since fairly successful cooling can be achieved.

### For Rotary Compressors:

- The Cooling is very difficult and Indices of less than are never achieved. It is therefore normal to compare the Performance with the Adiabatic reversible case.

## The Cooling Of Compressors.

It is usually considered that the heat is given up during the Compression: For a Polytropic Compression. For an Isothermal Compression.Example:

[imperial]

##### Example - Application of the gas laws to Air Compressors and Motors

Problem

An Air Compressor takes in Air at 14 psi and at 20 degrees C. It is compressed in accord to the law and delivers it to receiver at 140psi.
Find the Temperature at the end of the Compression and Calculate per pound of Air, the Compressor Work input and the heat rejected during Compression.

Workings

\therefore\;\;\;\;\;T_2=T_1\left(\frac{P_2}{P_1} \right)^{\frac{0.2}{1.2}}=293\left(\frac{140}{14} \right)^{\frac{0.2}{1.2}

=w\;R\times \left(\frac{n}{n-1 \right)\times \left(T_2-T_1 \right) }

Solution

Temperature at the end of the Compression
Compressor Work input
Heat Rejected during Compression