How to calculate the efficiency of a fuel engine

Homework Statement

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Im trying to find the efficiency of a gasoline engine regarded as a control volume. Am I right to use the HV as total energy input into the system?

Assuming the enthalpy of formation of the fuel cant be found.

I am really wondering if enthalpy of formation equals the enthalpy of a component at the temperature T = 298 K?

Mass flows of air, fuel are known.

Complete combustion is assumed.

Mass flow or molar flow of each component is multiplied with each corresponding enthalpy value to get the energy transfer per second

W_cv - Q_cv = HV + delta H_r - delta H p + H_r0 - H_p0

W_cv = work done by control volume [J/s] = mechanical work done by engine

Q_cv = heat exchange with surroundings [J/s]

where Q_cv = Q_exhaust + Q_engineheatloss

HV = Heat Value of the fuel [J/s]

delta H_p = sum of enthalpy difference of products relative to enthalpy of formation at 298 K [J/s]

delta H_r = sum of enthalpy difference of reactants relative to enthalpy of formation at 298 K [J/s] = 0

H_r0 = sum of enthalpies of formation of reactants [J/s]

H_p0 = sum of enthalpies of formation of products [J/s]

T_r = T_ambient = 298 K

T_p = T_exhaust = 773 K

Homework Equations

W_cv - Q_cv = HV + delta H_r - delta H p + H_r0 - H_p0

The Attempt at a Solution

As I understand it the total energy input into the engine would be the HV of the fuel, I assume this is equivalent to the value printed as energy content on the bottle/container following the fluid from the store.

To ease calculations I added up the enthalpies first in the below equation as I understood our professor, in such a way that I did not use massflow/molarflow rates of each component because I am correct when assuming that the sum of moles into the system equals the sum of moles out of the same system?::

H_r = H_p0 + HV

Finally I multiplied H_r with the molar flow of fuel into the system to get the total energy input which gave me different values when I used molar flow rates from the start (which makes me wonder if my calculations are wrong or method?)

So in order to find the efficiency of the engnine we are interested in the work done by the engine, W_cv.

Since efficiency in general is given by:

efficiency = useful work output /.total energy input = W_cv / HV

Also the energy lost through the exhaust would be I guess:
Q_exhaust = delta H_p

.

Last edited:

Nidum
Gold Member
I don't really see where you are going with this . You can define the efficiency of your 'engine' in one line .

Have you studied even basic thermodynamics ?

Last edited:
I don't really see where you are going with this . You can define the efficiency of your 'engine' in one line .

Have you studied even basic thermodynamics ?

Yes I have had a subject in thermodynamics at university last year. However we havn't gone through combustion in that course, just barely.

The equation from my thermodynamics book that we used in the course from a chapter that we did not go through is:
W_cv - Q_cv = HV + delta H_r - delta H p + H_r0 - H_p0

My professor that don't know so much about thermodynamics in our lab course claimed that the following is true:
H_r = H_p0 + HV is valid

Also she claimed that HV here would be the energy content value found on the bottle/container of the fuel.

I am simply wondering what I need in order to find the efficiency for the engine, in other words if it is correct to use the relation:
efficiency = useful work output /.total energy input = W_cv / HV

Where Work done by the engine is a value that is given. So in other words does HV represent the total energy input into the engine?