I have questions about Clausius's law. The specific questions are:

【My Questions】

  • (1)What and what is connected in “connected therewith” in 【Quote 1】 below?
  • (2) Give me some specific examples of "direct contact" and not "direct contact" in 【Quote 2】 below.

For question 1, Am I right if;
When "Heat transfer from the hot heat source to cold heat source" occurs, "some other change" always occurs at the same time?

For question 2, Am I right if;
Positive heat may flow from "cold heat source A" to the "high-temperature heat source B" only when there is a "region where the temperature cannot be determined" between the low-temperature heat source A and the high-temperature heat source B?

The original text of Clausius's principle is extracted below:

【Quote 1】 (ref.1)
”Heat can never pass from a colder to a warmer body without some other change, connected therewith, occurring at the same time. ”

A book has the following statement as a supplementary explanation of Clausius's principle.

【Quote 2】 (ref. 1)
" But with direct contact, even with man's intervention, heat can never pass from cold to warm."

(Ref.1) Block by Block: the Historical and Theoretical Foundations of Thermodynamics


1 Answer 1


Without seeing the quotes in context, in the first quote I believe “connected therewith” means a device located between the bodies (i.e heat pump/refrigerator).

In the second quote “direct contact” means without a such a device, such as heat transferring spontaneously by conduction from a cold cold to a hot body touching each other in violation of the second law.

Hope this helps

  • $\begingroup$ Thank you for your answer. It is very helpful. $\endgroup$ Commented Mar 20, 2020 at 11:28

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