Ch 21: The Second Law of ThermodynamicsWorksheetSee all chapters
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Ch 01: Units & Vectors
Ch 02: 1D Motion (Kinematics)
Ch 03: 2D Motion (Projectile Motion)
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Ch 05: Friction, Inclines, Systems
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Ch 20: The First Law of Thermodynamics
Ch 21: The Second Law of Thermodynamics
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Concept #1: Introduction to the Second Law of Thermodynamics

Concept #2: Introduction to Entropy and the Second Law of Thermodynamics

Example #1: Why Do Perfect Engines Violate the Second Law?

Practice: An engine operates with the following heat flow diagram. How much entropy is generated in each cycle?

Concept #3: Microstates and Macrostates of a System

Practice: The macrostate of a set of coins is given by the number of coins that are heads-up. If you have 100 coins, initially with 20 heads-up, what is Δ𝑆 when the system is changed to have 50 heads-up? Note that the multiplicity of k coins which are heads-up, out of N total coins, is Ω = 𝑁!/𝑘!(𝑁−𝑘)! . Does this change in macrostate satisfy the second law of thermodynamics?

Concept #4: The Second Law of Thermodynamics for an Ideal Gas

Additional Problems
n moles of an ideal gas expands while the temperature of the gas remains constant. In this process the entropy of the gas  (a) remains constant (b) decreases (c) increases
During an adiabatic change of state for an ideal gas 20 J of work are done on the surroundings. During this change, the temperature decreases from 400 K to 380 K. What is ΔU, ΔS and Q for this change of state? A. ΔU = 20J, ΔS = 0, Q = 0 B. ΔU = -20J, ΔS = 0, Q = 0 C. ΔU = 20J, ΔS = 20/390 J/K, Q = 0 D. ΔU = -20J, ΔS = 20/390 J/K, Q = 0 E. ΔU = 20J, ΔS = 20/390 J/K, Q = 20 J
A system takes in 200 J of heat while undergoing an isothermal change of state at 500 K. What is ΔU, ΔS, W, and Q for this change of state? A. ΔU = 0, ΔS = 1/2 J/K, W = 200 J, Q = 200 J B. ΔU = 0, ΔS = 2/5 J/K, W = -200 J, Q = -200 J C. ΔU = 200 J, ΔS = 1/2 J/K, W = -0, Q = 200 J D. ΔU = 0, ΔS = 2/5 J/K, W = -200 J, Q = 200 J
Using the Einstein model of a solid, what is the change in entropy when adding two quanta of energy to a system of 5 atoms that already has 5 quanta of energy stored in it? (In an Einstein solid each atom corresponds to three independent oscillators.) 1. ΔS = kB ln (21! /14! • 7!) 2. ΔS = kB ln (21/7 • 5) 3. ΔS = kB ln (17/6) 4. ΔS = kB ln (10/7) 5. ΔS = kB ln (10! /7!) 6. ΔS = kB ln (20! /14! • 5!) 7. ΔS = kB ln (20! /7! • 5!) 8. ΔS = kB ln (10)  9. ΔS = kB ln (21! /7! • 5!) 10. ΔS = kB ln (16!7! • 7)
An engineer claims to have built four engines. When operating between two reservoirs at 400 K and 300 K, the engines have the following characteristics:1) QH = 200 J, QC = -175 J, and W = 40 J2) QH = 500 J, QC = -200 J, and W = 400 J3) QH = 600 J, QC = -200 J, and W = 400 J4) QH = 100 J, QC = -90 J, and W = 10 JDo any of these engines violate either the first or the second law of thermodynamics?
A glass of water is left outside overnight to freeze. During this process, which of the following statements about entropy is true? A) The entropy of the surrounding air doesn't change overnight B) The entropy of the water changes more than the surrounding air overnight C) The entropy of the surrounding air changes more than the water overnight D) The change in entropy of the water is the same as the change in entropy for the surrounding air, with opposite signs
An ideal gas is taken through the cycle shown in the diagram below. The process is carried out with 150 mg of Helium, which is a monoatomic gas with an atomic mass of 4 g/mol. First, the gas undergoes an adiabatic expansion (from point A to point C), followed by an increase in pressure at constant volume (from point C to point B). Finally, the gas is taken back to the initial state by an isothermal compression (from point B to point A). What is the change in entropy of the gas during the isothermal process (from point B to point A)? Note that the work during an isothermal process is W = nRT ln(Vi / Vf).
Which of the following violates the second law of thermodynamics? (TH > TC) A. Heat taken from a body at TH is converted completely into work. B. Heat flows from a body at TH to another body at TC. C. Work is done to remove heat from a body at TC and exhaust it at TH. D. Heat taken from a body at TH is converted partly into work.
Blocks A and B have 300 and 200 oscillators, respectively. The blocks are placed in contact with each other in an insulated environment. At the instant the blocks touch, block A has 99 quanta of energy while block B has 1 quanta of energy. What will happen sometime after contact? I. The entropy of block A will increase. II. The entropy of block B will increase. III. The entropy of the two-block system will increase. 1. None 2. I, II only 3. II only 4. I, II, III 5. I, III only 6. II, III only 7. I only 8. III only