We were discussing Otto cycle, an ideal cycle for internal combustion spark ignition reciprocating engines or simply petrol engines, in our recent post. We have also discussed the derivation of efficiency of Otto cycle.

Today we will see here one more very important term i.e. volumetric compression ratio and simultaneously we will also see here the efficiency of Otto cycle in terms of volumetric compression ratio with the help of this post.

First we will have to see brief introduction and background to remind the concept of Otto cycle. 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.

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.

### Let us understand now the term volumetric compression ratio

Volumetric compression ratio will be defined as the maximum volume to minimum volume and it will be indicated by rv.
rv = V1/V2
Now we must have to understand here that why we are focusing here to understand the volumetric compression ratio and why we are giving stress to determine the result or formula to calculate the efficiency of the Otto cycle in term of volumetric compression ratio.

As we know very well that Otto cycle is one theoretical cycle or ideal cycle for internal combustion spark ignition reciprocating engines or simply petrol engines. Space is one design criteria for any automobile and automobile designer will have to surely consider this design criteria i.e. space restriction.

We will have to design our engine with considering the space permitted for respective automobile as we may not design one engine which accommodate large area as it will not be in favour of the user of automobile and therefore there will be one maximum volume and one minimum volume and we will have to design our engine with considering the maximum and minimum volume.

Now we will write here the expression of efficiency of the Otto cycle in terms of volumetric compression ratio.
So let us start to write few basic equations
PVγ= Constant
PV = RT
From above both equations, we will have
[V/T1/ (1-γ)] = Constant
As we have discussed in our recent post, efficiency of the Otto cycle will be determined with the help of following formula

T3/T4 = r (γ-1)
T2/T1 = r (γ-1)
Finally after using above value, we will have following formula to determine the efficiency of Otto cycle
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