Question

An Otto engine has a maximum efficiency of 33.1 %; find the compression ratio. Assume that the gas is diatomic.

Answer 1

For a diatomic gas, the specific heat ratio Cp/Cv = g = 1.4

The Otto cycle efficiency is available online as a function of g and the compression ratio, r. See

http://web.mit.edu/16.unified/www/SPRING/propulsion/notes/node25.html

The equation is

efficiency = 1 - 1/r^(g-1)

0.331 = 1- 1/r^(g-1)
1/r^(g-1)= 0.669
r^0.4 = 1.495
r = 2.73

I have never heard of an Otto cycle engine with a compression ratio that low, but that is what I get. Check for yourself

Answer 2

efficiency of Otto engine is
e= 1 –{V₂/V₁}^(γ-1)
γ=(i+2)/i
For diatomic gas i=5 =>γ=7/5=1.4
V₁/V₂= CR (compression ratio)
e= 1 –{1/CR}^(γ-1)=1-{1/CR} ^0.4

0.331 = 1-{1/CR} ^0.4

Solving for CR, we obtain CR=2.73

Answer 3

thank you guys,you helped a lot :)