Exercises: Moles, Combinatorics, and Large Numbers

Now is the time to apply what you have learned with practical exercises that will help you master essential thermodynamic concepts, such as moles, combinatorics, and calculations with large numbers. If you haven’t done so already, I recommend reviewing the previous lessons, as they contain the necessary foundations to approach these problems with confidence.

1. What is the mass of 3 moles of carbon dioxide (CO_2)? [SOLUTION]
2. A typical bacterium has a mass of 10^{-12}[g]. Calculate the mass of one mole of bacteria. [SOLUTION]
3. Estimate the number of water molecules in your own body. [SOLUTION]
4. A thermodynamic system has n atoms, each capable of having up to a single quantum of energy. How many different ways can k quanta of energy be distributed when:
   a) n=2 and k=1, [SOLUTION]
   b) n=20 and k=10, [SOLUTION]
   c) n=2\cdot 10^{23} and k=10^{23}, [SOLUTION]