A cup of hot coffee is placed inside a large, well-insulated container. Over a five minute...

A cup of hot coffee is placed inside a large, well-insulated container. Over a five minute period, the entropy of the cup decreases by 100 J/K. What can you say about the entropy of the air surrounding the cup?

Expert Solution

entropy of the Surrounding incraeses by more than 100 J/K since total entropy of universe is always increasing

Explanation:

The entropy of the surrounding air will increase by MORE than 100 Joules/Kelvin. Entropy is generated when heat is transferred across a finite temperature difference.

Suppose the coffee cup is at 360 Kelvin and the surroundings are at 300 Kelvin.

Suppose somehow the coffee remains at nearly constant temperature (don't ask me how). In reality it will change in temperature and we'd have a calculus problem, but that isn't the heart of my point.

Suppose that the coffee transfers 36000 Joules of heat to the surroundings, and the surroundings absorb this 36000 Joules.

The coffee releases an entropy(S = Q/T) of (36000 J)/(360 K), which is 100 Joules/Kelvin.
The surroundings absorb an entropy of (36000 J)/(300 K), which is 120 Joules/Kelvin.

Where did the 20 Joules/Kelvin come from? Well, it was entropy generated in the convection layer above the coffee surface. Heat transfer across a finite temperature gradient is an irreversible process and thus generates entropy

genius_generous answered 6 days ago

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