Thermo - Simple Energy balance equation

[ksukhin]

The General Energy balance equation is:
∑EN_in - ∑EN_out + E_gen = E_st (in rate form - don't know how to put the dot above)

I know that E_st is 0 when the system operates at Steady State Steady Flow (SSSF).

I have 2 formulas for ΔE in "Q-W = ΔE"
1) ΔE = ΔU + ΔKE + ΔPE
2) ΔE = m[h₂ - h₁ +(V₂-V₁)²/2 + g(z₂-z₁)]
How do I know which one to use in which scenario?

 

[Vatsal Sanjay]

1. ∑ENin - ∑ENout + Egen = Est

   Dude! There wouldn't be any $E_(gen)$ term in the energy equation. Energy cannot be created neither can it be destroyed. Though many textbooks write this term but this is not a good habit to follow. It destroys the whole beauty of energy conservation equation. What you interpret as $E_(gen)$ is actually the energy transformation from one form to other across the system boundary. For example suppose you have an electric heater of 1000 Watt. Instead of interpreting as 1000 J of energy being produced per second, you can interpret it as 1000 Joule of electric energy (from out of the system) coming inside the system and getting converted into heat energy, per second.
2. For your concern of which equation to use, I will suggest you to stop plugging equations in problems. Rather sit back and think about all the energy interactions going on for 1-2 minutes before actually starting the solution. The only reason, you see so many energy equations is because there are situations when one form of energy is negligible in comparison to others and hence are neglected. For example is the ( $v^2$ ) term is very small as compared to the enthalpy terms ( $h$ ), you can neglect the kinetic energy. You will know this once you choose your system and analyse it. Once you have identified, all the energies being involved, go for the energy conservation law. All you need to remember is that you cannot create energy out of nothing and that you cannot destroy it either.
   So the equation I prefer is $$ ∑E_(in) = ΣE_(out) + Δe $$ where $E_(in)$ involves all the energy coming inside the system in form of external work, heat input, enthalpy, kinetic energy of incoming fluid etc and similarly $E_(out)$ will include every outgoing energy. Further $Δe = e_(final)-e_(initial)$ where $e$ includes every energy associated with the substance inside the boundary. If you wish to write this in terms of rates, simply differentiate. The differentiation will be rather easy for a specific problem. I mean suppose I consider the enthalpy term, $H = m* h$ , where $h$ is the specific enthalpy, so in rate form this will simply be mass flow rate multiplied by specific enthalpy.

See in nutshell, all you need to do is know the energy transformations and trust the energy conservation law. Trust me, once you know how to use the energy conservation law properly, these equations will never bother you. You will get used to write your own equation for every case.

I have tried my best to be clear at what I am trying to convey, if there is something I have missed or something I am not clear at, please let me know.

 

[ksukhin]

Thanks for the quick reply!
I was a bit in shock since I have 8 finals in a span of 6 days so I blanked for a minute. I realized what I was doing wrong why i didn't get the equation.

I wasn't accounting for the work done by the fluid $pv$ and since $h=u+pv$ both equations are valid but they're case specific.

I was jumping from an Otto cycle which had Q_H=u₂-u₁ and a power plant where they use enthalphy. I just couldn't see that there was a $pv$ term not included because it wasn't needed.

Thanks again. I"m just a bit all over the place cause I'm freaking out

 

[Vatsal Sanjay]

Calm down buddy. I have been through same. However just for sake of completion (I think you already know this), $pv$ is not same as the work $∫p(dv)$ .

• $pv$ is the flow work and you are correct it comes into picture only when there is flow. Its mainly because of the change in pressure and volume of the fluid at the inlet and exit of a control volume (or any system in general)
• $∫p(dv)$ isthe boundary work associated with the change in volume of the system.

 

[ksukhin]

Calm down buddy. I have been through same. However just for sake of completion (I think you already know this), $pv$ is not same as the work $∫p(dv)$ .

• $pv$ is the flow work and you are correct it comes into picture only when there is flow. Its mainly because of the change in pressure and volume of the fluid at the inlet and exit of a control volume (or any system in general)
• $∫p(dv)$ isthe boundary work associated with the change in volume of the system.

Yup I see the difference now, thanks again! I'll do my best not to panic tomorrow haha

 

[Chestermiller]

In post #1,

The equations Q-W = ΔE and ΔE = ΔU + ΔKE + ΔPE comprise the version of the first law that apply to a closed system (no mass entering or leaving)

The equations ΔE =-m[h2 - h1 +(V2-V1)2/2 + g(z2-z1)]+Q-W_s and ΔE = ΔU + ΔKE + ΔPE comprise the version of the first law that apply to an open system (where mass can be entering and leaving). In this equation, W_s is the shaft work.

Chet