# Why is bringing two object to their initial temperature an irreversible process?

In the lectures, given in here, it is stated that

We can imagine thermodynamic processes which conserve energy but which never occur in nature. For example, if we bring a hot object into contact with a cold object, we observe that the hot object cools down and the cold object heats up until an equilibrium is reached. The transfer of heat goes from the hot object to the cold object. We can imagine a system, however, in which the heat is instead transferred from the cold object to the hot object, and such a system does not violate the first law of thermodynamics. The cold object gets colder and the hot object gets hotter, but energy is conserved. [...]

An example of an irreversible process is the problem discussed in the second paragraph. A hot object is put in contact with a cold object. Eventually, they both achieve the same equilibrium temperature. If we then separate the objects they remain at the equilibrium temperature and do not naturally return to their original temperatures. The process of bringing them to the same temperature is irreversible.

However, I can't understand why bringing those objects to their initial temperature is an irreversible process? I mean why shouldn't it be?

• In the process they describe doesn’t bring them to their original temperatures; it brings the to some temperature between their original temperatures. Jan 31, 2019 at 17:56
• @ChesterMiller Yes I can understand that, but they provide no argument for why can't we reverse the process by some means ? I mean "I don't know how to do it" is not valid argument, for example, so I would expect some physical argument that show it is impossible to do so.
– Our
Jan 31, 2019 at 17:58
• The issue is not that you can't do it, what it is saying is that it won't happen in an isolated system. If you have a hot object and a cold one, if you put them together they will come to a an equilibrium temperature in between. If you separate them, keeping the system isolated, they won't return to their initial hot and cold temperatures. Jan 31, 2019 at 18:12
• See additional paragraph in my answer, showing the reversible process. Jan 31, 2019 at 19:18

Sorry for my english !

You are talking about the principle principle of thermodynamics. Precisely, this is the Clausius statement : "It is impossible to construct a device which operates on a cycle and produces no other effect than the transfer of heat from a cooler body to a hotter body." https://www.ohio.edu/mechanical/thermo/Intro/Chapt.1_6/Chapter5.html

This is a principle, and it must be taken as such in the context of classical thermodynamics. Cinetic theory and statistical physics can help to understand it.

In the introduction to the chapter on the second law, in his book of thermodynamics, P. M. Morse analyse your questions on the fact that we can not prove the impossibility of doing something. I have copied some excerpt from "Thermal Physics", Morse, 1964 (Strong and Italic are mine !)

The laws of thermodynamics have a negative quality which distinguishes them from most other laws of physics, which makes direct, positive, experimental proof quite difficult. The first law may be phrased as saying that energy cannot be destroyed. This sort of negative is much harder to demonstrate than is the positive statement that gravitational force varies inversely as the square of the distance.......In a sense, we have to draw on the experience of all of physics to support the first law......

......The second law of thermodynamics also has this negative quality, and the lack of direct verification is even more noticeable than with the first law..... One way of phrasing the second law is that the spontaneous tendency of a system to go toward thermodynamic equilibrium cannot be reversed without at the same time changing some organized energy, work, into disorganized energy, heat. No single experiment will convince one of the validity of such a negative statement. All we can say is that the theory based on it, namely thermodynamics, has been and still is, successful in interpreting and predicting all thermal phenomena so far.

What they mean is that you will be able to return the bodies to their original states, but not without causing a change in the physical state of something else, like, for example, the states of one or more ideal constant temperature reservoirs. As an example, if you put the body that was originally higher in temperature into contact with a reservoir at its original higher temperature and the body that was originally lower in temperature into contact with a reservoir at its original lower temperature, then, in the end, both bodies will be at their original temperatures. However, the states of the two reservoirs will have changed. Even if you use more than two reservoirs (say at intermediate temperature), in the end the states of the various reservoirs will have changed.

If, instead of initially putting the two bodies into direct contact with one another to let them equilibrate, you kept them separate, and brought each of them into contact with a sequence of reservoirs (different for the high temperature body from the low temperature body) running gradually from their initial temperatures to their final temperatures (at the final equilibrium temperature they would have reached by allowing them to irreversibly equilibrate), this would have been a reversible process. You could have reversed this change and gotten both bodies back to their original states, as well as all the reservoirs.

Suppose the cold body started out at 0 C and its final temperature was 100 C. Now we wish to consider several alternate processes for raising the temperature of the cold body from 0 C to 100 C, and we want to see how close we can come to doing this reversibly (so that it can be returned to its initial state without significantly changing anything else).

The mass of the body is M and its heat capacity is C. We have at our disposal an array of 101 ideal constant temperature reservoirs, running in equal increments of 1 C, from 0 C for reservoir #0, to 100 C for reservoir #100.

PROCESS 1:

Forward path: Put body into contact with reservoir #100 and let them equilibrate. Heat transferred to body from reservoir 100 = 100MC

Reverse path: Put body into contact with reservoir #0 and let them equilibrate. Heat transferred to body from reservoir 0 = -100MC

The net result of this process for the forward and reverse paths is a transfer of 100MC heat from reservoir #100 to reservoir #0. So the process is far from being reversible.

PROCESS 2:

Forward path: Put body into contact with reservoir #50 and let them equilibrate. Heat transferred to body from reservoir #50 = 50MC. Then put body into contact with reservoir #100 and let them equilibrate. Heat transferred to body from reservoir #100 = 50MC.

Reverse path: Put body into contact with reservoir #50 and let them equilibrate. Heat transferred to body from reservoir #50 = -50MC. Then put body into contact with reservoir #0 and let them equilibrate. Heat transferred to body from reservoir #0 = -50MC.

The net result of this process for the forward and reverse paths is a transfer of 50MC heat from reservoir #100 to reservoir #0 (reservoir 50 remains unchanged). So the process is still pretty irreversible, but less so than Process 1, which results in a transfer of 100MC from reservoir #100 to reservoir #0.

Process 3:

Forward path: Put body into contact with reservoir #1 and let them equilibrate. Heat transferred to body from reservoir #1 = MC. Then put body into contact with reservoir #2 and let them equilibrate. Heat transferred to body from reservoir #2 = 1MC. Continue this through the sequence of reservoirs in 1 C increments until the body reaches 100 C.

Reverse path: Put body into contact with reservoir #99 and let them equilibrate. Heat transferred to body from reservoir #99 = -1MC. Then put body into contact with reservoir #98 and let them equilibrate. Heat transferred to body from reservoir #98 = -1MC. Continue this through the sequence of reservoirs in 1 C increments until the body reaches 0 C.

The net result of this process for the forward and reverse paths is a transfer of 1MC heat from reservoir #100 to reservoir #0 (all reservoirs in between remain unchanged). So this process is not nearly as irreversible as the other two processes which involved much larger temperature changes with many fewer reservoirs.

Now imagine extending this game plan to an infinite number of reservoirs in vanishingly small temperature changes. In this limit, the process becomes fully reversible.

• So, you say that this process is reversible ?
– Our
Feb 1, 2019 at 8:40
• Yes. Would you like me to explain in detail how this works? Feb 1, 2019 at 12:37
• Yes, I would definitely like to
– Our
Feb 1, 2019 at 14:14
• Ok. See addendum. Feb 1, 2019 at 16:03
• I have always disliked this argument: "However, the states of the two reservoirs will have changed." In my mind a "reservoir" is a boundary condition and as such does not change by the system under consideration. A battery in a circuit can be modeled as an ideal voltage source with an internal resistor. The source emf is then a boundary condition independent of the load attached to the terminals; the apparent change of the terminal voltage is to be attributed to the internal resistance not to the voltage source. The latter is then an effective boundary condition when applying Kirchhoff's laws. Feb 2, 2019 at 13:55