Physics 102 Lawrence Weinstein Homework Set 4 Solutions Chapter 15 Exercises: 42: If the temperature falls, then the water expands (and rises in the thermometer). If the temperature rises, then the water expands (and rises in the thermometer). Therefore, you can't tell whether the temperature is rising or falling. 46: 0 degrees: contract 4 degrees: expand 6 degrees: expand (No explanation is needed. If you look at the plot on p299 [fig 15.16] you can see that volume decreases from 0 to 2 degrees, increases from 4 to 6 and increases from 6 to 8 degrees.) ------------------ Chapter 16: Project 2: You need to explain two things: why you feel the heat, but the bulb stays cool. You feel the heat radiated by the filament inside the bulb. The bulb does not get hot instantly because it is transparent to the heat radiation. The heat radiated by the filament of the bulb is not absorbed by the bulb so the bulb does not get hot quickly. 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 conduction and heat capcacity. Heat conductivity is less important. 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. A bare potato is dark so it emits very well. The foil covered potato will have much smaller radiative heat losses. 16: When a hot object is placed in contact with a cooler object, heat flows from the hot object to the cooler object. Thus, the hot object loses just as much ENERGY as the cooler object gains. However, depending on the size and specfic heat capacities of the objects, the temperature changes will be different. For example, a hot rock placed in the ocean will cool down a lot and the ocean will only warm up very very little. 26: Both gases have the same temperature, therefore, the atoms of each gas have the same kinetic energy. Kinetic energy is KE = 1/2 mv^2. Since Krypton atoms have a larger mass than the argon atoms, they will have a smaller velocity to have the same kinetic energy. Thus, the argon atoms have a higher average velocity (move faster). 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 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. 40: The bench keeps the ground warmer the same way that nighttime clouds keep the Earth warmer. The ground radiates heat. It receives almost no heat radiation back from the night sky (at 4 K). If there is a bench over the ground, then the ground will receive heat radiation from the bench (which is MUCH warmer than the night sky). Thus, the part of the ground under the bench will be warmer than the part of the ground exposed to the night sky. Problems: 6: You need 3 kW of electric power. Each square meter of solar collector receives 200 W of sun light (on average). It can convert 10% of that to electricity. So each square meter of solar collector will provide 20 W of electric power. This means that you need 3000 W / 20 W/m^2 = 150 m^2 of solar collectors. Each m^2 is about 3x3 = 10 square feet. Thus, you need 1500 square feet of solar collectors. This is not much space. Almost all backyards are bigger than that (1 acre = 45 thousand square feet). --------------------- Estimation: The Earth is 6400 km in radius. This means that the disk of the Earth, as seen from the sun, is pi*r^2 = 3.14159 * (6400 km)^2 = 1.3*10^8 km^2 = 1.3 * 10^14 m^ in area. Thus, the power received is 1000 W/m^2 * 1.3*10^14 m^2 = 1.3 * 10^17 W. This is rather a lot. This is 100 million (10^8) large nuclear power plants.