Calculating Energy Lost Due to Flue Gases

[fantommass]

Hi!

I'm working on problem, where I have to estimate energy, lost due to flue gases, i.e. some amount of natural gases burned in some time period, say [t0;t1].
Burning is used for some material heating. I need to find energy, lost by gases (gases, after combustion), which goes out from flue. Heating is performed linearly, for example from point [0;100] to [2;400] (first coordinate is time in hours and second is temperature), so temperature dependence is like this:

T(t)=150t+100​

I was told that I have to calcule specific enthalpy change in order to calculate energy lost by fumes:

Q_f=MΔh_f​

where M is mass of fumes and Δh_f is specific enthalpy change.
Also I know that specific enthalpy depends on temperature throuth relation:

h_f(T)=0.28T-4.6​

So, for specified heating schedule, enthalpy depends on temperature through this:

h_f(t)=0.28(150t+100)-4.6=42t+23.4​

I'm I write, when I calculate change of specific enthalpy by integrating in time interval function h_f(t)?:

Δh_f=∫(42t+23.4)dt​

 

[Valerie Park]

=(42t^2/2+23.4t)|t0→t1And then I can calculate energy lost by fumes?Yes, that is the correct way to calculate the energy loss of the fumes. You would then use the change in specific enthalpy (Δhf) and the mass (M) of the fumes to calculate the energy lost: Qf = MΔhf.