# Machine in Clausius' 2nd law of thermodynamics?

• FranzDiCoccio
In summary, it is impossible to build a machine whose only effect is the transfer of heat from a heat reservoir to another heat reservoir at a higher temperature. This is a paraphrase of the 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."
FranzDiCoccio
Hi all,
sorry for the condensed title of my post. Any other version of the question I'm trying to ask turned out to be longer than allowed.

So, my question is about the wording in some versions of Clausius' statement of the 2nd law of thermodynamics.
From time to time I read something like "It is impossible to build a machine whose only effect is the transfer of heat from a heat reservoir to another heat reservoir at a higher temperature", possibly specifying "without any work done".

Perhaps I'm being nitpicking, but I have the feeling that the concept of "machine" does not fit well in Clausius' statement.
How is that a machine, if no work is involved?

I would rather say "a process where heat is spontaneusly transferred from a cold source to a hot source is impossible". Perhaps one could add "unless some work is done", but that's sort of covered by "spontaneously".

All in all it seems to me that sometimes authors are carried away a little and try to write Clausius' statement using the same wording as in Kelvin's one.
Is it just me? Or perhaps could it be a subtlety of Italian that does not emerge in English?

Are you ok with Clausius' formulation of the 2nd law involving a machine or a device?

The actual statement by Clausius appears to be
[I]Phil. Mag.[/I] 4. [B]12[/B] (77): 81–98 (1856) said:
Heat can never pass from a colder to a warmer body without some other change, connected therewith, occurring at the same time.
The 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.
can be found in many places, but I couldn't find a direct reference to anything Clausius wrote, so it is probably a paraphrase. Specifying the operation on a cycle appears to come from the previous work of Carnot.

FranzDiCoccio said:
Perhaps I'm being nitpicking, but I have the feeling that the concept of "machine" does not fit well in Clausius' statement.
How is that a machine, if no work is involved?
As you see, the quote I found mentions "device," not "machine." But I think that saying that a machine must do work is not appropriate in the context. It is to be considered more generally as a device that can do "things," that is not simply passive.

russ_watters
Hi DrClaude,

I see what you mean, and I agree that a device is not necessarily a machine involving work.

It is probably a sloppy translation from English to Italian. In a textbook I read "a thermal machine" where "a device" should be.
I find that confusing, because a thermal machine makes me think of something involving mechanical work.

I'd rather say "a thermal process".

FranzDiCoccio said:
I'd rather say "a thermal process".
That wouldn't do it for me. I think that the word "device" is the most appropriate. The problem with "thermal process" is that it seems to imply that only heat is involved, while the device can include something like a piston compressing a gas.

russ_watters
Wait, wouldn't that mean that some work is done/produced?

You mean you could in principle do "useless" actions like compressing the gas and expanding it back so that the net work is zero?

FranzDiCoccio said:
Wait, wouldn't that mean that some work is done/produced?
No, when let my coffee cool before drinking it, it isn't doing any work, it is just sitting there transferring heat to the surroundings.

And not for nothing, but while an air conditioner as an overall device transfers heat from a low temperature to a high temperature area, none of the individual processes do. That's how the violation is avoided.

russ_watters said:
No, when let my coffee cool before drinking it, it isn't doing any work, it is just sitting there transferring heat to the surroundings.
Hi Russ,

but there's no piston acting on your coffee while it gets spontaneously colder.

What I mean is that my comment about work is in relation to DrClaude's comment
the device can include something like a piston compressing a gas.
And not for nothing, but while an air conditioner as an overall device transfers heat from a low temperature to a high temperature area, none of the individual processes do. That's how the violation is avoided.

Uhm... I agree that none of the individual processes in an air conditioner does that. But some of those processes do involve work, and the total amount of work is negative (injected in the system). And that's how the violation is avoided.

I mentioned the word process, because clearly there exist processes whose only effect is the transfer of heat from a hotter source to a colder one.
I was thinking that, all in all, Clausius statement can be worded as "you cannot expect heat to flow spontaneously from cold to hot. If you want that, you need to spend some energy". I was going to say "some work", but I guess that devices like a Peltier cell would fit into this.

Again, I'm ok with the word device.
I'm still not convinced by "thermal machine" . Are you ok with a version of the Clausius' statement that goes like

"It is impossible to construct a thermal machine which operates on a cycle and produces no other effect than the transfer of heat from a cooler body to a hotter body."?

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## 1. What is the Machine in Clausius' 2nd law of thermodynamics?

The machine in Clausius' 2nd law of thermodynamics refers to any device or system that converts heat energy into mechanical work. This law states that heat cannot spontaneously flow from a colder body to a hotter body, and that the efficiency of any heat engine is always less than 100%.

## 2. How does the machine relate to the 2nd law of thermodynamics?

The machine is a key component in understanding and applying the 2nd law of thermodynamics. It serves as an example of a system that is subject to the law's principles, namely the conversion of heat into work and the direction of heat flow.

## 3. What is the significance of the machine in thermodynamics?

The machine is significant because it helps to illustrate the limitations and constraints of the 2nd law of thermodynamics. It also serves as a practical application of the law, as many real-world devices and systems operate based on these principles.

## 4. Can the machine violate the 2nd law of thermodynamics?

No, the machine cannot violate the 2nd law of thermodynamics. This law is a fundamental principle of thermodynamics and has been extensively tested and proven through experiments and observations. The machine must adhere to this law, just like any other system.

## 5. How does the machine's efficiency relate to the 2nd law of thermodynamics?

The efficiency of a machine is directly related to the 2nd law of thermodynamics. This law states that no machine can have an efficiency of 100%, meaning that some of the heat energy will always be lost in the process of converting it into work. The efficiency of a machine is a measure of how well it adheres to this law.

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