phys124s11-hw12

phys124s11-hw12 - HW 12 Solutions From Hot to Cool The...

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HW 12 Solutions From Hot to Cool: The Second Law of Thermodynamics a) What happens to the entropy of a bucket of water as it is cooled down (but not frozen)? 0 < = Q T Q dS δ It increases. It decreases. It stays the same. b) What happens to the entropy of a cube of ice as it is melted? 0 > = = Q T mL T Q dS melt It increases. It decreases. It stays the same. c) What happens to the entropy of a piece of wood as it is burned? Both kinetic energy of molecules and the volume occupied by the molecules increase – the multiplicity (and, thus, the entropy) increases. It increases. It decreases. It stays the same. d) An object at 20 0 C absorbs 25.0 J of heat. What is the change in entropy Δ S of the object? K J K J T Q dS / 0853 . 0 293 25 = = = e) An object at 500 K dissipates 25.0 kJ of heat into the surroundings. What is the change in entropy Δ S of the object? Assume that the temperature of the object does not change appreciably in the process. K J K J T Q dS / 50 500 10 25 3 = = = f) An object at 400 K absorbs 25.0 kJ of heat from the surroundings. What is the change in entropy Δ S of the object? Assume that the temperature of the object does not change appreciably in the process. K J K J T Q dS / 5 . 62 400 10 25 3 = = =

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g) Two objects form a closed system. One object, which is at 400 K, absorbs 25.0 kJ of heat from the other object, which is at 500 K. What is the net change in entropy Δ S sys of the system? Assume that the temperatures of the objects do not change appreciably in the process. K J K J K J T Q T Q S S S sys / 5 . 12 500 10 25 400 10 25 3 3 2 2 1 1 2 1 = = + = Δ + Δ = Δ δ Heat Engines Introduced a) A heat engine is designed to do work. This is possible only if certain relationships between the heats and temperatures at the input and output hold true. Which of the following sets of statements must apply for the heat engine to do work? and and and and b) Find the work W done by the "ideal" heat engine. Express W in terms of h Q and c Q . c h Q Q W = The thermal efficiency e of a heat engine is defined as follows: h Q W e / = . Express the efficiency in terms of h Q and c Q . h c h h Q Q Q Q W e = Test Your Understanding 20.3: Internal-Combustion Engines If you double the compression ratio of an Otto-cycle engine from 6.0 to 12, what happens to the engine's thermal efficiency? it decreases it remains the same it increases by a factor greater than 2 it increases by a factor of 2 it increases, but by a factor less than 2 it increases, but not enough information is given to decide by what factor The thermal efficiency e of an Otto-cycle engine with compression ratio r is 1 1 1 = γ r e
where 4 . 1 = γ is the ratio of heat capacities for air. For 6 = r we find 51 . 0 = e and for 12 = r we find 63 . 0 = e . Thus the efficiency increases, but by a factor less than 2. Test Your Understanding 20.8: Microscopic Interpretation of Entropy

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phys124s11-hw12 - HW 12 Solutions From Hot to Cool The...

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