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Can a “miserly” system, with a concave-up entropy-energy

An Introduction to Thermal Physics | 1st Edition | ISBN: 9780201380279 | Authors: Daniel V. Schroeder ISBN: 9780201380279 40

Solution for problem 4P Chapter 3

An Introduction to Thermal Physics | 1st Edition

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An Introduction to Thermal Physics | 1st Edition | ISBN: 9780201380279 | Authors: Daniel V. Schroeder

An Introduction to Thermal Physics | 1st Edition

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Problem 4P

Problem 4P

Can a “miserly” system, with a concave-up entropy-energy graph, ever be in stable thermal equilibrium with another system? Explain.

Step-by-Step Solution:
Step 1 of 3

ANSWER:

For the concave up entropy-energy graph, the slope is negative.

And we know that,

     

  • This indicates negative temperature which is not defined generally, but at a higher level we understand negative temperature.

  • Negative temperature is more hotter than infinite temperature.

  • It occurs when you add more heat to a system and increase the internal energy of it without any work done, the entropy of the system decreases. This decrease in entropy is not very often in day to day life but very rare events.

  • But such systems do exist in nature.

  • Note that, negative temperature does not mean that . it is in absolute kelvin scale.

  • So far we know that the zero kelvin is the lowest temperature in nature.

  • Negative temperature is negative in kelvin scale.

Conclusion:

So, this system with negative temperature cannot be in equilibrium with any other system.

Step 2 of 3

Chapter 3, Problem 4P is Solved
Step 3 of 3

Textbook: An Introduction to Thermal Physics
Edition: 1
Author: Daniel V. Schroeder
ISBN: 9780201380279

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Can a “miserly” system, with a concave-up entropy-energy