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.

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**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 r

_{v}.
r

_{v}= V_{1}/V_{2}
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

PV

^{γ}= Constant
PV = RT

From above both equations, we will have

[V/T

^{1/ (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)}
T

_{2}/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.

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**Reference:**

Engineering thermodynamics by P. K. Nag

Engineering thermodynamics by Prof S. K.
Som

Image courtesy: Google