Carlos Gouveia said:
Hey, whoa. Evaluating the entropy change between two thermodynamic states is one thing. For this your step-by-step procedure above seems to be adequate. But I was talking about measuring entropy discretely -- like taking the temperature of my office as I write this, right now. How do I measure the entropy of the air (in J/(K kg) ) in my office right now? I know thermometers, barometers and so on, but I totally ignore the existence of an entropy-o-meter. Entropy is a property of state, so it is defined at any pressure-temperature pair (I might resort to an air entropy chart and check what is S at 99,000 Pa and 18 C, but that's not measuring something at all). Got my point?
By the way, the Step 3 above involves the evaluation of an integral (numerically, I presume, and probably over a broken path). That completely screws up the whole concept of measuring.
Hopefully we are not sliding into the swamp of semantics and making a bit of a mess between the words measure, calculate, evaluate &c.
We have indeed slid into a swamp of semanitcs (initiated by you). In post #5, you said: "
I think you can't measure entropy but you can certainly calculate it." If you meant that entropy is a property that can't be measured
directly, then you should have said
directly. But, that would have negated your counter-example of specific heat, which also cannot be measured directly. (see your Post #3:
That doesn't happen with the specific heat of some substance or body, which you can measure"). I don't think you are aware of a meter that can measure specific heat directly.
Specific heat is defined as the partial derivative of either internal energy or enthalpy with respect to temperature, either at constant volume or at constant pressure, respectively. Each of these can be obtained by determining the heat flow in a related process, and differentiating the cumulative heat flow with respect to temperature. But this involves the calculation of a derivative, which constitutes a calculation just as much as the determination of the entropy change involves calculation of the integral of dq
rev/T. So, while not involving direct measurement, they certainly both involve measurement.
It is silly to think that the geniuses who developed thermodynamics (e.g., Clausius) would have been interested in a quantity that can't be measured, but only calculated. Even if the entropy of a substance is calculated using values of the heat capacity, the latent heats of phase changes, and the P-V-T behavior of the substance, this is certainly equivalent to measuring the entropy of the substance. The determination of the entropy change from one state to another using the method of step 3 does indeed involve a calculation of the integral of dq
rev/T, but, as I indicated above, the determination of the heat capacity of a substance also involves a calculation, namely the derivative of the cumulative heat flow with respect to temperature. How can one of these be called a calculation, and not the other? Both of these constitute a measurement of thermodynamic state function.
If you are unhappy with what I said about determining the
change in entropy of a substance from one state to another, rather than the absolute value of the entropy (which you seem to have brought into the discussion in response #10), then I refer you to the literature on the Third Law of Thermodynamics.
Smith and Van Ness, Introduction to Chemical Engineering Thermodynamics: "the absolute entropy is zero for all perfect crystalline substances at absolute zero temperature. While the essential ideas were advanced by Nernst and Planck at the beginning of the twentieth century, more recent studies at very low temperature have increased our confidence in this postulate, which is now accepted as the third law."
Hougen, Watson, and Ragatz, Chemical Process Principles, Part II: "It was proposed by Nernst and subsequently confirmed by extensive experimentation that at the absolute zero of temperature the entropy of a pure crystalline substance free of all random arrangement is zero. Accordingly, by extending measurements of specific and latent heats down to 0 K, absolute values of entropy can be calculated"
If the entropy is zero at T = 0 K, then the integral of dq
rev/T can be used to calculate the absolute entropy of a substance at any other state. But this certainly involves measurement of the heat flow over a reversible path. So, if you want to know the entropy of the air in your room, all you need to do is follow this procedure for both the nitrogen and the oxygen, and then include the entropy of mixing for ideal gases.
In order to avoid further confusion and misinformation, I am hereby closing this thread.
Chet
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