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« Last post by **MJM460 ** on* ***Today** at 01:12:47 PM »
Well at least the plumbing issue is resolved and fixed. No amount of theory will predict that the tube had not been pushed far enough into a quick-lock fitting. But something made me look very carefully into the fitting, make some measurements and stick a little bit of tape on the tube to mark the correct insertion. I had just not used enough muscle. I had to get that out of the way before discussing entropy.

I have avoided mentioning entropy up until now but Willy, your post last night suggests it is on your mind, so let's have a go. The page you scanned from your book made a quite suitable introduction.

You may remember that I described enthalpy as a property that only depended on pressure temperature pressure and specific volume, all things we can measure. It did not depend on the previous history of how the substance came to have that particular pressure, temperature and specific volume. That sentence is basically the definition of a property. I noted that enthalpy is calculated from the pressure temperature and specific volume, we don't have an enthalpy meter. But the calculation of enthalpy comes into many significant problems and thermodynamics (particularly problems involving heat and work, so obviously interesting to anyone designing and operating heat engines). It is so useful that it is convenient to have the value tabulated in steam tables, and the tables for other fluids such as refrigerants.

Entropy is another such calculated property, given the symbol S. No such thing as an entropy meter, it is the outcome of a calculation. I think the main reason that entropy is so mysterious is that it is not a simple calculation involving things we can measure, but it requires a bit more complex calculation that has a surprising applicability. The calculation involves summing the quotient of heat input divided by temperature as a substance undergoes an ideal reversible process, which goes in such small steps that the temperature can be considered constant within each step. In symbols it is written

dS = dQ / T at each step, and leads to the result that e change of entropy with the process (S2-S1) is found by integration of dQ/T through the process. Now none of us want to have to do integral maths to understand our engines, but we don't have to. The unexpected result is that this change in entropy, even though it is calculated by considering an ideal reversible process, is exactly the same, whether the process was reversible, or ideal, or was not reversible. The reversible process allows the change to be calculated, but then the result also applies to any real irreversible process as well. So we can leave it to a few boffins to calculate the values and include them in our steam tables, and tables for other fluids.

Now apart from the interesting unexpected nature of this property, why do we care? It comes down to the second law of thermodynamics. If we first note that the first law calculates the heat exchanged in a process based purely on conservation of energy, but gives us no idea of whether the process can actually occur. For example we can calculate the heat lost by your tea to your teaspoons when you plunge them in to the hot brew. The first law tells is that it is the same amount as is gained by the spoons. But we can also calculate how much heat would be gained by the coffee if it became hotter by cooling the teaspoons. Now we know that can't happen. The second law of thermodynamics tells us it can't happen, but does not really quantify why it can't happen. This is where entropy comes in. It turns out that the only processes that can happen (without heat or work input) are processes that result in an increase of entropy. This is relatively easily extended to mean that the entropy of the universe is increasing. Philosophers ponder if there is a limit, if so what happens when the limit is reached, or is there a mechanism somewhere in the universe that reverses the increase of entropy. But I find all that way too esoteric. I would rather leave such discussions to someone who cares.

However, accepting the concept of entropy, and having it tabulated in steam tables is very useful. So let me illustrate by showing how it helps us understand a steam engine. Let's assume we have a boiler, and the steam outlet pipe then loops back through the fire box a couple of times as a superheater, then on to the engine. We can measure the temperature and pressure at the engine inlet. We would all like to know how much work our engine can produce. We need to know the exhaust pressure, but we don't know the exhaust temperature. We know the amount of work is given by the change of enthalpy, but we need to evaluate that change. Now we remember that ideally steam expansion in an engine is an adiabatic process, meaning no heat transfer in or out. And it turns out that an ideal or adiabatic process also means no change in entropy. So if we look up the entropy of our steam at the engine inlet, it will have the same value at the exhaust of our adiabatic engine. With a bit of interpolation of the steam tables, we can find the temperature, and enthalpy of the exhaust steam, and also the exhaust steam quality or dryness if the exhaust is wet steam. Now we can easily calculate the change in enthalpy by subtraction.

Using entropy, just using the tabulated values in the steam tables, has allowed us to calculate the power output of an ideal engine. The second law of thermodynamics tells us that any real engine will produce less power than an ideal or adiabatic one. This leads to a definition of adiabatic efficiency, but that can come another time.

Now your other comments, letting the air out when your element is inserted. Your explanation seems likely. It would take some ingenuity, but it should be possible to devise a way to solder a return bend on the end of your reamed tube, and use say 3 mm tube vent back to the mounting flange. This would allow you to use the grease. But your other suggestions to reduce the time to raise steam? I am tempted to stick my neck out and suggest the only way to raise steam quicker is to put in more heat, either use a bigger element, or put in two or three elements. You see your heater power rating is the amount of heat generated by the element per unit time. A 500 Watt element means 500 Joules/second. We have previously looked at how to calculate how much heat is required to heat water from cold, say 15 deg C to saturation temperature, and we can look up the specific heat of copper and calculate the heat required to increase the copper temperature from 15 to our operating temperature. You have an advantage over fired boilers, you know how much heat is produced and you can insulate it well to limit loss to the atmosphere, though we should make an estimate of the heat that will be absorbed by the insulation. So you only need to weigh the empty boiler, and the quantity of water you fill , and you can calculate the time required. Similarly, once you start steam production, you can calculate the heat required per kg of steam, and so you can easily determine how much steam you can make with 500 watts, as no more heat is absorbed by the copper or insulation once steady temperature is reached. All your effort to improve the heat transfer coefficient only reduces the temperature the element must reach to transfer the rated heat. It does not affect the time to heat or the the amount of steam you can raise. So long as you insulate the boiler well! I will hold the air questions until I get to condensers, and try and address Pauls comments tomorrow.

Paul, you have obviously understood well my explanation of how heat is changed to work in our engines. I will address your questions on this next time.

Oh and thanks for the notice about the Mildura conference. Mildura is about 600 km from Melbourne, quite a solid drive. Unfortunately I have too many other commitments in October, but it's good to see these events being held "locally".

MJM460