1. What is the ideal efficiency of an automobile engine in which fuel is heated to 2700 K and the outdoor air is 270 K?
2. Consider an ocean thermal energy conversion (OTEC) power plant that operates on a temperature difference between deep 4°C water and 25°C surface water. Show that the Carnot efficiency of this plant is 7%.
3. On a chilly10°C day, your friend who loves cold weather says she wishes it were twice as cold. Taking this literally, show that the temperature she wishes for would be -131.5°C.
4. Imagine a giant dry-cleaner's bag full of air at a temperature of -35°C floating like a balloon with a string hanging from it 10 km above the ground. Estimate what its temperature would be if you were able to yank it suddenly back to Earth's surface.
5. Calculate the ideal efficiency of an engine wherein fuel is heated to 2700 K and the surrounding air is 300 K.
6. Wally Whacko claims to have invented a heat engine that will revolutionize industry. It runs between hot sources at
300°C and a cold sink at 25°C. He claims that his engine is 92% efficient.
(a) What error did he make in his choice of temperature scales?
(b) What is the actual maximum efficiency of his engine?
7. A power station with an efficiency of 0.4 generates 108 W of electric power and dissipates 1.5 x 1081 of heat energy each second to the cooling water that flows through it, which increases its temperature by 3 Celsius degrees. Knowing that the specific heat of water in SI units is 4184 J/kg.°C, show that 12,000 kg of warmed water flows through the plant each second.
8. Construct a table of all the possible combinations of numbers that can come up when you throw two dice. Your friend says, "Yes, I know that 7 is the most likely total number when two dice are thrown. But why 7?"
Based on your table, answer your friend, and explain that, in thermodynamics, the situations that are likely to be observed are those that can be formed in the greatest number of ways.