How Is Entropy Measured in Thermodynamics?

[24forChromium]

When I learned the concept of specific heat capacity, I knew that 1J/(K*kg) means that it takes 1 Joule of energy to increase the temperature of a kilogram of matter by one Kelvin, but what does J/K, the unit of entropy, mean?

 

[ShayanJ]

You can't understand it using its units. I suggest you to read this book.

 

[Carlos Gouveia]

What does J/Pa mean to you? To many people it might seem as meaningless as J/K at a first sight. However, J/Pa translates into volume since ΔW/p = ΔV,where W is work, p is pressure and V is volume. I think part of "meaninglessness" of entropy comes from the fact that you can't measure it as you could measure pressure, temperature and volume, for example (and that's what the four basic Maxwell relations are good for). And it is usually hard to get the meaning of something you cannot measure. That doesn't happen with the specific heat of some substance or body, which you can measure -- and that's perhaps why you understand the "meaning" of that property. Well, that's just my opinion.

 

[Chestermiller]

What does J/Pa mean to you? To many people it might seem as meaningless as J/K at a first sight. However, J/Pa translates into volume since ΔW/p = ΔV,where W is work, p is pressure and V is volume. I think part of "meaninglessness" of entropy comes from the fact that you can't measure it as you could measure pressure, temperature and volume, for example (and that's what the four basic Maxwell relations are good for). And it is usually hard to get the meaning of something you cannot measure. That doesn't happen with the specific heat of some substance or body, which you can measure -- and that's perhaps why you understand the "meaning" of that property. Well, that's just my opinion.

Who says you can't measure the entropy change of a system between two different thermodynamic equilibrium states? In fact, it can be measured in a way very similar up how you measure the heat capacity.

Chet

 

[Carlos Gouveia]

Who says you can't measure the entropy change of a system between two different thermodynamic equilibrium states? In fact, it can be measured in a way very similar up how you measure the heat capacity.

Chet

I think you can't measure entropy but you can certainly calculate it.

 

[rootone]

An entropy meter would be a very useful tool.

 

[Chestermiller]

I think you can't measure entropy but you can certainly calculate it.

This is not correct. So please don't give your opinion on technical issues unless you are sure. Misinformation like this merely confuses the member who originally posted.

One certainly can measure the change in entropy between two thermodynamic equilibrium states of a system. It can be measured almost as easily as measuring the heat capacity.

Chet

 

[Carlos Gouveia]

This is not correct. So please don't give your opinion on technical issues unless you are sure. Misinformation like this merely confuses the member who originally posted.

One certainly can measure the change in entropy between two thermodynamic equilibrium states of a system. It can be measured almost as easily as measuring the heat capacity.

Chet

Cool. So enlighten me and tell me how this is done. Since you seem to suggest that it's a measurement I assume that this is carried out in a lab. Serious, I'm curious about that procedure.

 

[Chestermiller]

Cool. So enlighten me and tell me how this is done. Since you seem to suggest that it's a measurement I assume that this is carried out in a lab. Serious, I'm curious about that procedure.

No problem. You wish to measure the difference in entropy between two thermodynamic equilibrium states of a system (where the transition between these states may have taken place irreversibly).

Step 1: Dream up a reversible path between these same two thermodynamic equilibrium states (which may not necessarily bear any resemblance to the actual path for the transition). Any reversible path will suffice.

Step 2: Carry out an experiment that measures the small changes in the heat transferred between the surroundings and the system dq along this reversible path and the corresponding temperatures along the path.

Step 3: Evaluate the integral of dq/T. This is the change in entropy ΔS between the two end states.

You may wish to read my recent Physics Forums Insights article on this subject at the following link: https://www.physicsforums.com/insights/understanding-entropy-2nd-law-thermodynamics/

Chet

 

[Carlos Gouveia]

No problem. You wish to measure the difference in entropy between two thermodynamic equilibrium states of a system (where the transition between these states may have taken place irreversibly).

Step 1: Dream up a reversible path between these same two thermodynamic equilibrium states (which may not necessarily bear any resemblance to the actual path for the transition). Any reversible path will suffice.

Step 2: Carry out an experiment that measures the small changes in the heat transferred between the surroundings and the system dq along this reversible path and the corresponding temperatures along the path.

Step 3: Evaluate the integral of dq/T. This is the change in entropy ΔS between the two end states.

You may wish to read my recent Physics Forums Insights article on this subject at the following link: https://www.physicsforums.com/insights/understanding-entropy-2nd-law-thermodynamics/

Chet

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.

 

[Chestermiller]

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.

I don't have time to respond to this right now (grandchildren visiting), but I will be responding in detail sometime during the coming week (probably Sunday). Sorry for the delay, but...I'll Be Back.

Chet

 

[Jimmy Moriaty]

J/K represents the energy that increases when the temperature increased by 1 unit.
Simply entropy describes the instability of a system.(That's energy )

 

[Chestermiller]

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