MATSE 201 (Introduction to Materials Science and Engineering)
HW4: Thermodynamics (100 pts.)
For full credit clearly state your approach, assumptions, and calculation steps. Use units where
needed and clearly mark your answer. Upload your solutions as a .pdf file to Canvas.
1. Laws of Thermodynamics
a. Write the 1st law of thermodynamics in differential form for a closed system. (6 pts.)
b. If a system gains heat from the surroundings, is dQ positive or negative? If a system does
work on the surroundings, is dW positive or negative? (4 pts.)
c. Write an expression for the 2nd law of thermodynamics (either classical or statistical
mechanics). (6 pts.)
d. The “Heat Death of the Universe” is a potential fate of the universe. Explain how this
hypothesis is arrived at based on the 2nd law of thermodynamics as well as what type of
system it assumes the universe to be. (14 pts.)
2. Entropy
a. Define the term “entropy”. (6 pts.)
b. Rank the following systems from least to most entropy, assuming the same temperature:
liquid, gas, solid. (12 pts.)
c. Assume that you have a system consisting of three boxes (A, B, and C) and two particles
(R and B) that can be placed into the boxes (each box can hold both particles, one, or none).
i. Draw all distinct microstates for this system. (10 pts.)
ii. Calculate the entropy of this system. (10 pts.)
3. State Functions
a. Define the term “state function”. (6 pts.)
b. Of the following, identify which are state functions and which are path functions: “heat”,
“elevation”, “volume”, “temperature”, “work”, “distance travelled”, “pressure”, “internal
energy”, “Gibbs free energy”. (10 pts.)
c. Explain how the Gibbs free energy can still be negative (spontaneous) for an endothermic
(+ΔH) reaction. (10 pts.)
d. Define the term “free energy”. (6 pts.)