Heat Capacity Ratio and Thermal Efficiency

[lmse]

I'm taking an internal combustion class this semester and the professor asked the class why the thermal efficiency increases when you increase the heat capacity ratio even though the area on the P-V diagram for an Otto cycle, and thus the work created by the process, decreases. It's obvious from the thermal efficiency equation that this is true but i'm not exactly sure what my professor is trying to get at. Since the work, which is the output, decreased according the P-V diagram, while the thermal efficiency increased, I must assume that the input decreased even more rapidly. I'm not sure how these all tie together. Any help would be much appreciated.

 

cheers,

 

Laurens

 

[studiot]

Well I assume you have the equation for the efficiency, which does indeed show that

 

[math]e = 1 - \frac{1}{{{r^{y - 1}}}}[/math]

Since the compression ration, r is greater than 1.

 

In the derivation of this equation use is made of the fact that the compressions are isentropic (adiabatic) so that the expressions

 

[math]\frac{{{T_2}}}{{{T_1}}} = \frac{{{T_3}}}{{{T_4}}} = {r^{y - 1}}[/math]

 

hold good. These are used along with the basic definition for efficiency (output/input) to derive the above expression.

 

So the short answer to your question is becasue the two compressions are isentropic (adiabatic).