Editing Compressor (section)

====Effect of cooling during the compression process====
[[File: Insetropic,polytropic,isothermal.jpg|thumb|P-v (Specific volume vs. Pressure) diagram comparing isentropic, polytropic, and isothermal processes between the same pressure limits.]]

[[isentropic]] process: involves no cooling,<br />
[[polytropic]] process: involves some cooling<br />
[[isothermal]] process: involves maximum cooling

By making the following assumptions the required work for the compressor to compress a gas from <math>P_1 </math> to <math> P_2</math> is the following for each process:
<br />













: <math>P_1 </math> and <math> P_2</math>

: Flow processes VdP
: All processes are internally reversible
: The gas behaves like an [[ideal gas]] with constant [[specific heats]]

Isentropic (<math> Pv^k = constant </math>, where <math>k = C_p/C_v</math>):
<br />
: <math> W_{comp,in}= \frac{kR(T_2-T_1)}{k-1}=\frac{kRT_1}{k-1} \left [  \left ( \frac{P_2}{P_1} \right ) ^{(k-1)/k} -1 \right ] </math>

Polytropic (<math> Pv^n = constant </math>):
<br />
: <math> W_{comp,in}= \frac{nR(T_2-T_1)}{n-1}=\frac{nRT_1}{n-1} \left [  \left ( \frac{P_2}{P_1} \right ) ^{(n-1)/n} -1 \right ] </math>

Isothermal (<math>T = constant</math> or <math>Pv = constant</math>):
<br />
:<math> W_{comp,in}= RT ln \left (  \frac{P_2}{P_1}\right ) </math>

By comparing the three internally reversible processes compressing an ideal gas from <math>P_1 </math> to <math> P_2</math>, the results show that isentropic compression (<math> Pv^k = constant </math>) requires the most work in and the isothermal compression(<math>T = constant</math> or <math>Pv = constant</math>) requires the least amount of work in. For the polytropic process (<math> Pv^n = constant </math>) work decreases as the exponent, n, decreases, by increasing the heat rejection during the compression process. One common way of cooling the gas during compression is to use cooling jackets around the casing of the compressor.<ref name="Cengel, Yunus A. 2012"/>