Friday, 11 November 2016

OTTO CYCLE EFFICIENCY DERIVATION

OTTO CYCLE EFFICIENCY DERIVATION

We were discussing Otto cycle, an ideal cycle for internal combustion spark ignition reciprocating engines, in our recent post. We have also discussed basic operations and arrangements of various components of ideal cycle for internal combustion spark ignition reciprocating engines. We have also seen there the PV diagram for an Otto cycle.

 
Today we will see here the calculation of efficiency of Otto cycle with the help of this post.

Otto cycle: Efficiency

Otto cycle is one type of air standard cycle which is designated as the ideal cycle for the operation of internal combustion spark ignition reciprocating engines. Before understanding the method for determination of the efficiency of the Otto cycle, we will have to remind here various processes involved.

Therefore first let us see an overview of an Otto cycle with the help of PV diagram and TS diagram as displayed here in following figure. As we can see in below figure, there will be two isentropic or adiabatic processes and two constant volume processes. We will determine the various properties for unit mass of working fluid.

Process 1-2: Compression stroke

Let us use the concept of first law of thermodynamics
Q= ΔU + W
 
As we have already seen that process 1-2 will follow constant entropy process and therefore Q= 0
Hence we will have from first law of thermodynamics ΔU = - W
ΔU = CV (T2-T1)
W = CV (T1-T2)

Process 2-3: Combustion stroke

As we have already seen that process 2-3 will follow constant volume process and therefore W= 0
Q= ΔU = CV (T3-T2)
Hence, heat energy addition to the system Q = Q1 = CV (T3-T2)

Process 3-4: Expansion or power stroke

As we have already seen that process 3-4 will follow constant entropy process and therefore Q= 0
Hence we will have from first law of thermodynamics ΔU = - W
ΔU = CV (T4-T3)
W = CV (T3-T4)

Process 4-1: Blow down

 
As we have already seen that process 4-1 will follow constant volume process and therefore W= 0
Q= ΔU = CV (T1-T4)
Hence, heat energy rejection from the system Q = Q2 = CV (T4-T1)

Efficiency of the Otto cycle

Efficiency of the Otto cycle will be determined with the help of following formula
Do you have any suggestions? Please write in comment box.
We will see another topic in our next post in the category of thermal engineering.

Reference:

Engineering thermodynamics by P. K. Nag
Engineering thermodynamics by Prof S. K. Som
Image courtesy: Google

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