A Swirling Vortex of Entropy

Classical Mechanics Level 3

At a reasonably high (and equal) temperature, one mole of which of the following has the greatest entropy?

Both have equal entropy. Carbon dioxide Dioxygen

Agnishom Chattopadhyay by Agnishom Chattopadhyay , 22, India

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1 solution

Dioxygen is a diatomic gas. How does one uniquely state the configuration of a dioxygen molecule?

There are six degrees of freedom. You need three parameters to locate the first atom, two more to locate the second, and one more to specify the vibration of the bonds.

Carbon dioxide is triatomic linear.

There are seven degrees of freedom. Three to locate the first atom and two for the second. This fixes the third atom. We need two more for the two bonds.

There are more ways to distribute energy amongst the Carbon dioxide molecules.

This is why it has higher entropy.

Reality Check!

Standard Molar Entropy for Oxygen: 205.15 J/mol/K

Standard Molar Entropy for Carbon Dioxide: 213.79 J/mol/K

Source

3 Helpful 0 Interesting 0 Brilliant 1 Confused

Yup, the right way to think about this is degrees of freedom. Nice little problem.

Jake Lai - 5 years, 6 months ago

What are degrees of freedom?

Bhavya Sheth - 5 years, 6 months ago

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It is the number of pieces of information you require to accurately describe an objects configuration.

E.g, an atom in space has three degrees of freedoms since you need three coordinates to describe it. A lizard on a wall has three degrees of freedoms too, two for its location, a third for the position of its tail

Agnishom Chattopadhyay - 5 years, 6 months ago

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