Physics 102 Homework Set 5 Solutions Chap 18 Exercises: 2: No, it does not matter. If I tell you that the temperature is 20 degrees, then it matters whether it is Kelvin or Celsius, since 20 K is as cold as Pluto and 20 C is room temperature (20 C = 293 K). But if the temperature is 10,000,000 degrees, then it does not matter. There is no significant difference between 10,000,273 degrees and 10,000,000 degrees. The 273 difference is insignificant. 18: The efficiency of an ideal heat engine is (T_hot - T_cold)/T_hot. Thus, if you increase T_hot or you decrease T_cold, then the efficiency will increase. 20: The thermal energy is dumped into the cold reservoir. Thus, if that temperature is lowered (ie: decreasing T_cold), then the efficiency will increase. 26: There are two effects. 1) in a warm room, more heat will leak into the refrigerator (since the insulation is not perfect). Thus, there are more Joules of heat to remove. 2) The heat to be removed has to be pumped out to a higher temperature. It is harder to pump heat from a 40 degree F refrigerator to an 80 degree room than to a 60 degree room. Thus, the refrigerator has to do more work to remove each Joule of heat. 28: If the building is electrically heated, it does not matter whether that heat comes from light bulbs or heaters since 100% of the electrical energy ends up as heat in either case. (Note that this does not apply to a building heated by gas or oil. In this case, 100% of the energy from the gas is converted to heat. However, if the gas is burned to generate electricity, only about 1/3 of the energy in the gas is converted to electricity. Thus, it is more efficient to heat your house with gas than with electricity. [Note that this does not apply to heat pumps.]) It IS wasteful to leave the lights on when you are air conditioning the building. In that case, the lights add heat to the building. The AC has to work harder to remove that heat from the building to keep it cold. 36: No, this does not violate the principle of entropy. You can use energy (ie: do work) to reduce entropy in a limited system. (For example, if you work hard, you CAN clean your room.) The chicken uses the energy in food to reduce its entropy. In effect, it dumps the extra entropy into its excrement. 38: The probability of getting both heads in 2 coins is 1/2 * 1/2 = 1/4. In ten minutes = 600 seconds, you will throw the coins about 600 times. In 600 tries, they will surely come up both heads at least once. The probability of getting more heads is as follows: 1 2 3 4 5 6 7 8 9 10 1/2 1/4 1/8 1/16 1/32 1/64 1/128 1/256 1/512 1/1024 or (1/2) raised to the tenth power. In one hour = 3600 seconds, you can throw ten coins about 1000 times. This means that you are likely to get all heads about once. (The probability is 1/1000 and you repeat it 1000 times.) The probability of getting 10,000 heads is (1/2) raised to the power 10,000. This is about (1/1000) raised to the power 1000 (since 1/2 raised to tenth power is 1/1000). This is an unbelievably tiny number. There is no way you will get this many coins to be all heads if you spend your entire life throwing coins. 40: Use your judgement Problems: 2: The ideal efficiency is (T_hot - T_cold) / T_hot = (2700 - 270)/2700 = 0.9. 6: The power station has to dump 150,000,000 Joules of energ yeach second to the water. The water has a heat capacity of 4186 J/kg-C and each kg is heated by 3 C. This means that each kg absorbs 3 * 4186 = 12558 J and the plant needs 1.5 * 10^8 J/s / 1.26 * 10^4 J/kg = 1.2 * 10^4 kg/s of water (or 12 tons per second). Estimation: The power plant generates 1 Billion Watts. In one year, it generates 1*10^9 J/s * 365 days/year * 24 hours/day * 3600 seconds/hour = 3 * 10^16 J (rather a lot). It has an efficiency of 1/3 so it needs three times as much input thermal energy to generate that much useful output. This means that it must burn fuel containing 9 * 10^16 J each year. Coal contains about 10^7 J/kg so it needs about 9 * 10^9 kg of coal. This is 9 Million tons or 90,000 railroad cars (or almost 300 railroad cars each and every day). Uranium releases about 10^14 J/kg through nuclear fission so the power plant needs only 900 kg of uranium each year or about 1 ton. Yes, radioactive waste is horrible and dangerous. But there's a LOT less radioactive waste produced from a nuclear plant than there is coal ash and smoke from a coal plant. You're a voter. You choose.