An Otto engine has a maximum efficiency of 33.1 %; find the compression ratio. Assume that the gas is diatomic.
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
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
thank you guys,you helped a lot :)
To find the compression ratio for an Otto engine with a given maximum efficiency, we can use the formula for the maximum thermal efficiency of an Otto cycle:
η_max = 1 - (1 / r^(γ-1))
Where:
η_max is the maximum thermal efficiency
r is the compression ratio
γ is the ratio of specific heat capacities for the gas
In this case, since the gas is assumed to be diatomic, the value of γ is 1.4.
Substituting the given value of η_max = 0.331 and γ = 1.4 into the equation, we have:
0.331 = 1 - (1 / r^(1.4-1))
Now, we can solve for r.
Let's rearrange the equation:
1 / r^(1.4-1) = 1 - 0.331
1 / r^(0.4) = 0.669
Taking the reciprocal of both sides:
r^(0.4) = 1 / 0.669
Now, we can find the value of r by raising both sides of the equation to the power of 1/0.4:
r = (1 / 0.669)^(1/0.4)
r ≈ 9.7
Therefore, the compression ratio for the Otto engine is approximately 9.7.