## Activity Based Physics Thinking Problems in Thermodynamics: Energy

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### Activity Based Physics Thinking Problems in Thermodynamics: Energy

 1) You see a penny lying on the ground. A penny won't buy much these days, so you think: 'If I bend down to pick it up I will do work. To do that work I will have to burn some energy. It probably costs me more to buy the fuel (food) to provide that energy than I would gain by picking up the penny. It's not cost effective.' You pass it by. Is the argument correct? Estimate the energy cost for picking up a penny. You may find the following information useful: A jelly donut contains about 250 Calories (1 Calorie = 1 Kcal). 2) Converting typical kinetic energies we are used to into thermal energy typically produces small rises in temperature and that this was in part responsible for the difficulty in discovering the law of conservation of energy. It also implies that hot objects contain a lot of energy. (This latter comment is largely responsible for the industrial revolution in the 19th century.) To get some feel for these numbers, carry out three estimates: (a) A steel ball is dropped from a height of three meters onto a concrete floor. It bounces a large number of times but eventually comes to rest. Estimate the ball's rise in temperature. (b) Suppose the steel ball you used in part (a) is at room temperature. If you converted all its internal energy to kinetic energy, how fast would it be moving? (Give your answer in units of miles per hour. Also, ignore the fact that you would have to create momentum.) (c) Suppose a nickel-iron meteor falls to the earth from deep space. Estimate how much its temeprature would rise on impact. 3) For each of the situations described below, the object considered is undergoing some changes. Among the possible changes you should consider are: (Q) The object is absorbing or giving off heat. (T) The object's temperature is changing. (U) The object's internal energy is changing. (W) The object is doing mechanical work or having work done on it. For each of the situations described below, identify which of the four changes are taking place and write as many of the letters Q T U W (or none) as are appropriate. a) A cylinder with a piston on top contains a compressed gas and is sitting on a thermal reservoir (a large iron block). After everything has come to thermal equilibrium, the piston is moved upward somewhat (very slowly). The object to be considered is the gas in the cylinder. b) Consider the same cylinder as in part a, but it is wrapped in styrofoam, a very good thermal insulator instead of sitting on a heat reservoir. The piston is pressed downward (again, very slowly), compressing the gas. The object to be considered is the gas in the cylinder. c) An ice cube sitting in the open air is melting. 4) If you drink cold water it will soon warm up to body temperature (about 37 °C). This takes energy. Therefore, you ought to be able to keep your weight down even if you eat fattening food provided you also drink lots of cold water. Estimate what volume of cold water you would need to drink to overcome the effect of eating one chocolate sundae (about 500 Cal). 5) (a) When a molecule of a liquid approaches the surface, it experiences a force barrier that tries to keep it in the liquid. It thus has to do work to escape and loses some of its kinetic energy when it leaves. Assume that a water molecule can evaporate from the liquid if it hits the surface from the inside with a kinetic energy greater than the thermal energy corresponding to the temperature of boiling water, 100 oC. Use this to estimate the numerical value of the work 'W' required to remove a water molecule from the liquid. (b) Even though the average speed of a molecule in water below the boiling point corresponds to a kinetic energy less than 'W', some molecules leave anyway and the water evaporates. Explain why this happens. 6) An intensive variable is one that can be defined locally within a system; its magnitude does not depend on the boundaries selected for the system. An extensive variable is one that is defined for the system as a whole; its magnitude does depend on the boundaries selected for the system. Which of the following variables are intensive and which are extensive? Explain your reasoning in each case. (a) density; (b) pressure; (c) volume; (d) temperature; (e) mass; (f) internal energy; (g) number of moles; and (h) molecular weight.

These problems written and collected by E. F. Redish. These problems may be freely used in classrooms. They may be copied and cited in published work if the Activity Based PhysicsThermodynamics Problems site is mentioned and the URL given. Web page created and edited by K. A. Vick.

To contribute problems to this site, send them to redish@physics.umd.edu.

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