Chapter 12The Laws of ThermodynamicsQuick QuizzesAnswers to Even Numbered Conceptual QuestionsAnswers to Even Numbered ProblemsProblem SolutionsThe Laws of Thermodynamics 431Chapter 12The Laws of ThermodynamicsQuick Quizzes1. (b). The work done on a gas during a thermodynamic process is the negative of the area under the curve on a PV diagram. Processes in which the volume decreases do positive work on the gas, while processes in which the volume increases do negative work on the gas. The work done on the gas in each of the four processes shown is:54.00 10 JaW =- �, 53.00 10 JbW =+ �, 53.00 10 JcW =- �, and 54.00 10 JdW =+ �Thus, the correct ranking (from most negative to most positive) is a,c,b,d.2. A is isovolumetric, B is adiabatic, C is isothermal, D is isobaric.3. (c). The highest theoretical efficiency of an engine is the Carnot efficiency given by1c c he T T= -. Hence, the theoretically possible efficiencies of the given engines are:A700 K1 0.3001 000 Ke = - =, B500 K1 0.375800 Ke = - =, and C300 K1 0.500600 Ke = - =and the correct ranking (from highest to lowest) is C, B, A.4. (b). 0rQSTD = = and 0Q = in an adiabatic process. If the process was reversible, but not adiabatic, the entropy of the system could undergo a non-zero change. However, in that case, the entropy of the system’s surroundings would undergo a change of equal magnitude but opposite sign, and the total change of entropy in the universe would be zero. If the process was irreversible, the total entropy of the universe would increase.5. The number 7 is the most probable outcome because there are six ways this could occur: 1-6, 2-5, 3-4, 4-3, 5-2, and 6-1. The numbers 2 and 12 are the least probable because they could only occur one way each: either 1-1, or 6-6. Thus, you are six times more likely to throw a 7 than a 2 or 12.432 CHAPTER 12Answers to Even Numbered Conceptual Questions 2. Either statement can be considered an instructive analogy. We choose to take the first view. All processes require energy, either as energy content or as energy input. The kineticenergy which it possessed at its formation continues to make Earth go around. Energy released by nuclear reactions in the core of the Sun drives weather on Earth and essentially all processes in the biosphere. The energy intensity of sunlight controls how lush a forest or jungle can be and how warm a planet is. Continuous energy input is not required for the motion of the planet. Continuous energy input is required for life becauseenergy tends to be continuously degraded, as energy is transferred by heat into lower-temperature sinks. The continuously increasing entropy of the Universe is the index to energy-transfers completed. 4. Shaking opens up spaces between the jelly beans. The smaller ones have a chance of falling down into spaces below them. The accumulation of larger ones on top and smaller ones on the bottom implies an increase in order and a decrease in one contribution to the total entropy. However, the second law is not violated and the total entropy of the system increases. The increase in the internal energy of the system comes from the work required to shake the jar of beans (that is, work your muscles must do, with an increase in entropy accompanying the biological process) and also from the small loss of gravitational potential energy as the beans settle together more compactly. 6. Temperature = A measure of molecular motion. Heat = the process through which energyis transferred between objects by means of random collisions of molecules. Internal energy= energy associated with random molecular motions plus chemical energy, strain potential energy, and an object’s other energy not associated with center of mass motion or location. 8. A higher steam temperature means that more energy can be extracted from the steam. Fora constant temperature heat sink at cT and steam at hT, the maximum efficiency of the power plant goes as 1h c ch hT T TT T-= - and is maximized for high hT.10.max80 K22%373 KhTeTD= = � (Assumes atmospheric temperature of 20°C.)12. An analogy due to Carnot is instructive: A waterfall continuously converts mechanical energy into internal energy. It continuously creates entropy as the organized motion of thefalling water turns into disorganized molecular motion. We humans put turbines into the waterfall, diverting some of the energy stream to our use. Water flows spontaneously from high to low elevation and energy is transferred spontaneously from high to low temperature by heat. Into the great flow of solar radiation from Sun to Earth, living thingsput themselves. They live on energy flow. A basking snake diverts high-temperature energy through itself temporarily, before it is inevitably lost as low-temperature energyThe Laws of Thermodynamics