Physics 102 Homework set 4 Solutions L. Weinstein Exercises: ---------- 15.2: A Celsius degree is larger. 1 degree C = 1.8 degree F. 15.6: The molecules in a gram of steam are at a higher temperature than the molecules in the ice and therefore have a higher average kinetic energy. 15.10: Yes, this also applied when you drop a hot rock into the Atlantic Ocean. The rock will cool (a lot) and the water will warm (but only a very little bit) 15.16: A kilogram of iron undergoes a greater temperature change than a kilogram of water when a certain amount of heat is added to it. This is because water has a much larger specific heat capacity (thermal inertia) than iron (this means that it takes much more energy to change the temperature of water by a certain amount than to change the temperature of a comparable amount of iron). 15.26: If the wind blew mainly from the East, then Washington DC would get the wind that blows in from over the Atlantic Ocean. This would moderate the temperature of the wind (since the ocean water temperature does not go below freezing in the winter and does not get very hot in the summer) and would therefore make Washington's climate much more moderate (warmer in the winter and cooler in the summer). San Francisco, on the other hand, would get the wind that blows in from over the land so its temperature would vary much more than it does today. 15.28: Since the temperature of desert sand changes so much, it indicates that its specific heat is very small. (The desert gets the same amount of energy from sunlight as other regions and it loses the same amount of energy at night. Since it has the same energy input and output, but its temperature changes a lot more, this indicates that its spefific heat is very small.) 15.40: The gas meter measures the volume of gas that you use. If the gas is warmer when it passes through the meter, then the same amount of gas will occupy more volume and you will pay more money (PV = nRT). This will benefit the gas company. 15.52: If water is used in a thermometer and the temperature is 4 degrees C, then the water will expand if the temperature increases or decreases. In either case, the water level in the thermometer will rise. 16.2: Feather beds trap a lot of air. Air is a very good insulator. Therefore, a feather bed will trap the body heat you emit and keep you warm. 16.6: No, cold does not flow. Heat flows from your hand, through the nail, to the ice. You feel the loss of heat as 'cold'. 16.14: The air and the walls of the pizza oven are at the same temperature. However, the air is a very poor heat conductor and the walls are good heat conductors. Therefore, if you hold your hand in the oven for a few seconds, very little heat will be conducted to your hand. If instead you touch the walls of the oven, a LOT of heat will be conducted to your hand very quickly. Ouch! 16.18: Heat flow depends on temperature, not internal energy. (And temperature is related to the average KINETIC ENERGY of the molecules, not the internal energy. Internal energy also includes vibrational and rotational energy.) Yes, heat can flow between two objects with the same internal energy. A kilogram of water and a kilogram of iron that have the same internal energy will have very different temperatures. The water will have a much lower temperature because it has a much higher specific heat capacity. Alternatively, if your two objects are a 1-kg iron block and a 10-kg iron block, then the 1-kg block will have to be at about ten times the temperature to have the same internal energy as the larger block. Yes, heat can flow from an object of smaller internal energy to an object with larger internal energy. If you have a 1-kg block of iron that has half the internal energy of a 10-kg block of iron, then the 1-kg block will be at a temperature about 5 times higher. Problems: ----------------- 16.6: I get 200 W/m^2. This means that each square meter receives 200 W of power (or 200 Joules every second). I can convert 10% of that to electricity, so I get 20 W/m^2 of electrical power. I need 3 kW = 3000 W of power. Therefore, I need an area of A = 3000 W / (20 W/m^2) = 150 m^2. This is about 1500 ft^2 or an area 40 ft wide by 40 feet long. Yes, this will fit in a typical yard. Estimation: ------------ A typical American eats between 2000 and 3000 food calories per day so I'll use 2500 C. Now we need to convert to Joules per day (note that 'C' stands for food calorie and 'c' stands for regular calorie): 2500 C/day = 2.5*10^3 C/day * (1000 c / 1 C) * (4 J / 1 c) = 10^7 J/day We want the answer in Watts (J/s) so we need to calculate the number of seconds in a day: heat output = 10^7 J/day * (1 day / 24 hours)*(1 hour/60 minutes)*(1 min / 60 s) = 1*10^2 J/s = 10^2 W You emit about as much heat as a 100 W light bulb.