Physics 102 Lawrence Weinstein Homework Set 4 Solutions Chapter 15: Exercises: 10: The rock transfers heat to the water. This decreases the temperature of the rock and increases the temperature of the water. If the water is just a pail of water, then the temperature rise will be significant. If the water is the Atlantic ocean, then the temperature will still rise, but it will be too small to measure. 20: The jug of water would be better. It has a higher heat capacity. This means that it can transfer more heat to you (keeping you warm) before its temperature drops too far and it gets cold. 26: The air pressure in the tires increases because they heat up (with no change in volume). They heat up because of friction between the tires and road. More precisely, they heat up because the tire flexes as it rotates and this flexing heats up the tire. Modern tires are designed to reduce this kind of friction (so as to improve gas mileage). 34: The iron ring expands when it is heated. After it is slipped over the cold brass cylinder, the iron cools and contracts, the brass heats and expands. This means that the iron grips the brass incredibly tightly (since it exerts a tremendous force on the brass). 42: If the temperature falls from 4 C to 3 C, then the water expands (and rises in the thermometer). If the temperature rises from 4 C to 5 C, then the water expands (and rises in the thermometer). Therefore, you can't tell whether the temperature is rising or falling. ------------------------- Chapter 16: Exercises: 2: 70 degree F air feels warm to us because the heat from our body warms a blanket of air around us (this is the blanket of air that can be blown away by the wind, causing wind chill). It takes very little heat from our body to warm this blanket. 70 degree F water feels cool to us because it takes a lot more heat from our body to make a warm blanket of water around us (since water has a MUCH higher specific heat capacity than air). As we swim, we have to keep heating more water (as we swim away from the previously warmed blanket of water). The important concepts here are heat conduction and heat capacity. Radiation is irrelevant. 6: The foil gets as hot as the potato so that it cannot affect conductive or convective heat transfer. (ie: a foil covered potato and a bare potato will conduct and convect the same amount of heat). However, the foil is shiny (very reflective) so it does not emit well (it does not radiate a lot of energy). A bare potato is dark so it emits very well. The foil covered potato will have much smaller radiative heat losses. 9: Snow is white so it reflects solar radiation. The gravestone is dark so it absorbs solar radiation and heats up. The warm gravestone melts some of the snow next to it. 12: When your fingers are next to the flame, the energy transfer comes from radiation and from conduction. There is very little energy transferred by conduction since air is a good insulator. When your fingers are above the flame, energy is also transferred by convection as the hot gasses of the flame rise. 34: Two kinds of radiation comes from objects: the radiation they reflect and the radiation they emit. A good emitter of radiation is also a good absorber (which means that it does not reflect much radiation). Thus, the good emitter absorbs the light that hits it and does not reflect much light. It emits a lot of radiation, but at room temperature this radiation is infrared and cannot be seen by the human eye. 38: There are two effects here. I will accept either or both as the correct answer. The coffee is initially very hot. Therefore, it transfers a lot of heat to the adjoining air because there is a large temperature difference between the coffee and the air. (Remember that the larger the difference in temperature, the more heat is transferred.) If you add the cream immediately, then average temperature of the coffee plus cream is lower, there is a smaller temperature difference between the cream+coffee and the adjoining air, and less heat is lost to the air. Since less heat is lost to the air when you add cream quickly, the coffee will be hotter if you add cream now rather than waiting. The second reason is that coffee by itself is black. This means that it is a good emitter and radiates a lot of energy. When you add the cream, it lightens the color significantly so that the coffee radiates less energy. This is a much smaller effect than the first one. ---------------------------- Problems: Chapter 16: 6: 200 W of sunlight falls on each square meter of solar panel but the solar panels can only convert 10% or 20 W to electrical power. Since you need 3 kW or 3000 W, this means that you will need 3000 W Area = ------ = 150 m^2 20 W/m^2 That is a square a little more than 12 m or about 40 feet on a side. Most back yards are large enough. ------------------------------ Estimation: To calculate my power output, I need the amount of energy I consume. Let's assume that I eat 2500 Calories per day. Thus I eat E = 2.5 * 10^3 Cal = 2.5 * 10^6 cal * (4 J/cal) = 1 * 10^7 J each day. Now we need the number of seconds in one day because power is energy divided by time: 1 day = 24 hours/day * 60 minutes/hour * 60 seconds/minute = 8.6 * 10^4 sec Therefore my power output is P = 10^7 J / 8.6*10^4 sec = 120 W This is about the same as a 100 W light bulb.