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## 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

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