Physics 132 Online Homework Problem: Chapter 3 Problem 1. (Thermodynamic Equilibrium) Pick all the correct statements about thermodynamic equilibrium a. Thermodynamic equilibrium is a static equilibrium b. Thermodynamic equilibrium is a dynamic equilibrium C. At thermodynamic equilibrium, the energy in each degree of freedom is the same d. At thermodynamic equilibrium, the probability of finding a certain amount of energy is the same in each degree of freedomProblem 2. (Counting the Degrees of Freedom) A. For a monatomic molecule like He, shown below, determine the number of quadratic degrees of freedom it has. X B. For a diatomic molecule like N2, determine the maximum number of quadratic degrees of freedom it can have.C. For a linear triatomic molecule like CO2, determine the maximum number of quadratic degrees of freedom it can have. D. Determine the number of quadratic degrees of freedom of CO2, at a temperature such that the vibrational degrees are not excited. E. Consider two identical rigid containers containing an equal number of moles of gas: one containing O2 and one containing CO2 . The temperature of both gases is high enough that vibrational modes of both gases are activated. If the temperature of each container changes by the same amount, the change in internal energy of 02 is denoted by AU.2, and the change in internal energy of CO2 is denoted by AUco2, what is the ratio AUO2 AUco? ?Problem 3. (Heat Capacity and Degrees of Freedom) A. A calorimeter is used to measure the heat capacity of two molecules, A and B. Molecule A is a simple small molecule, whereas molecule B is a complex polymer (like DNA). Which molecule is most likely to have a higher heat capacity? a. Molecule A b. Molecule B B. To understand the Part A of this question more quantitatively, let's say that Molecule A has 20 degrees of freedom, and molecule B has 2 x 105 degrees of freedom. Calculate the heat capacity for each of molecules A and B. Express your answers in units of i. Molecule A: ii. Molecule B: C. Going the other way, if we know the heat capacity of a molecule, we calculate the number of degrees of freedom that it has. Consider a gas molecule X. X's heat capacity is 4.14 X 10-23 J/K. i. Calculate the number of degrees of freedom of X ii. Given that some degrees of freedom may not be activated, X could be: a. Monatomic b. Diatomic c. TriatomicProblem 7. (Dice and Coins) A bored student at a coffee shop has a fair coin and a fair six-sided die in their pocket and idly rolls the die and then flips the coin. A. What is the probability that the die rolls a 4 and the coin ends up heads? The student then comes up with a game to pass the time using the coin and die, as follows: First, the student rolls the die. If the roll is odd, they flip the coin once. If the roll is even, they flip the coin twice. They then score the coin flips: if the coin comes up heads it's worth 1 point, and if it comes up tails its worth zero points. This ends the round, and then another round can be played. After each round, the possible scores can be 0, 1, or 2. B. What is the multiplicity of the "2" macrostate? That is, how many different arrangements of die rolls + coin flips would result in a score of 2? (Hint: It will be easiest to write out each of the possible outcomes that lead to this score, rather than trying to come up with some formula for it.)