4 replies to this topic

[Lolly84]

Right. This should be very straightforward, but I'm not sure whether I'm over-thinking this, or if I'm just being plain stupid, and I'm getting myself into a bit of a tizz about not quite getting this concept. Help would be hugely hugely appreciated, as I've been trawling through internet sites and c+r trying to find an explanation that would clarify things to me, and I'm at the end of my tether.

So. Specific heat capacity. The amount of heat required to raise the temperature of a unit mass by 1deg.
Fair enough. However, I would like to calculate the amount of energy that would be removed from a system by cooling a process gas from 200 deg C to around 80 deg C. I guess my main question is, which specific heat value do I use? Do I use a middle ground, so, the specific heat capacity for each component of my gas stream at 140 degC is used, multiply by the temperature difference (120 degC) and multiply by the relative mass flow of each component, and then sum all of these individual energy losses? This is what the literature I've found has said to do. But, I'm confused because surely if the specific heat capacity of a material is changing as its temperature changes, surely this calculation needs to be more of an integral, or should be able to take into account the changing specific heat capacity - particularly over such a large temperature difference.

So, then I thought, well, can you say that you can work out the energy of the process gas at 200 degC, by summing the individual component calculations of m x 200 x specific heat capacity of component at 200 degC, then do the same for each component at 80 degC and use the specific heat capacity of each component at 80 degC. Will subtracting the second value away from the first value give you the energy difference ie the amount of energy that needs to be removed from the gas in order for it to reach 80 degC?

I've tried going back to basics and manipulating the Q=mcpdeltaT equation in different ways and plugging in various numbers, but I still can't seem to understand.

I guess, what I'm asking is, is it safe to assume an "average" specific heat capacity value, and if so, why? Is there a more accurate method which takes into account the changing cp over such a temperature range?

Help would be so so very much appreciated, I'm getting so frustrated with myself that I've not got this clear in my head, because it doesn't seem like it should be a problem!

Thanks in advance.

[Zauberberg]

Lolly,

The way you asked this question is almost magic, and it brings back a lot of good memories.

Cp can be defined as the change in the enthalpy of a substance per unit change in temperature at constant pressure. In other words, Cp is a measure of the variation of enthalpy of a substance with temperature: Cp = Cp(T). We can assume that your system pressure is constant, and the only thing which is the subject of change is - temperature. If you want to do this in an academic manner, you should then develop a set of equations describing Cp behavior from initial temperature to the final temperature - depending of fluid composition. And there are lot of textbooks which can give you a guidance in this subject. But, what is the use of this approach? What is the main purpose of your calculations? Cooler design? Deviations of approximated values versus integrated values? Developing a heat capacity VS temperature equation for particular gas mixture?

The basic rule in engineering is to keep your calculations as simple as possible, with as low error as possible. If you are designing a gas cooler, weighted average heat capacity is quite good enough: the average value derived from mixture heat capacity at the end of cooler, plus the capacity at the inlet of gas cooler, derived by two (since the mass flow is unchanged). This assumption relies on linear heat capacity change with temperature - and in most of applications without phase change you can rely on this approach.

Lolly
I suggest you to read Thermodynamics- Van Ness Smith.
Cp/R = A+BT+CT^2+DT^-2

A, B,C, D are constants for the gas in question. You can find these constants in the same txt book. Then integrate Cp over the range 200 to 80. Then the heat lost equals mass*Cp.

Alternately, you can refer Perry. There's an equation at the end of the Cp tables in hyperbolic functions. Use this at 200 and 80. Then average it. Now heat lost equals mass*Cp*deltaT

Hope this clarifies your question.

".........can you say that you can work out the energy of the process gas at 200 degC, by summing the individual component calculations of m x 200 x specific heat capacity of component at 200 degC, then do the same for each component at 80 degC and use the specific heat capacity of each component at 80 degC. Will subtracting the second value away from the first value give you the energy difference ie the amount of energy that needs to be removed from the gas in order for it to reach 80 degC...."

This doesnt work because heat content is m*Cp*deltaT and not m*Cp*T

[kiwiland]

Hi

I did Falling Film Humidifier experiment its that wetted-wall column one. I hve a question regarding specific heat capacity. I was told to calculate Delta Q and mCpdeltaT separately and then write what relationship it shows. After my calculations, the values for mCpdelta T are higher than Delta Q ...so wht do I write about the relationship and also the reason for it.

Also just to make sure the units for mCpDelta T are KJ Dry Air / min Kelvin ?

I would really appreciate your help.

cheers