Warm-Up Exercise 11

Due 12:15 pm, Fri 21 Sep 2012

Physics 123, Fall 2012

Why would you want to use a heat pump (instead of an electric heater) to heat your house when 100% of the energy in an electric heater can be converted directly to heat? Isn't that more efficient? Explain.

The heater converts 100% of the used energy into heat, but the heat pump can *move* an amount of energy from outside the house to inside the house. For a given energy expended, heat pumps are able to move more energy than electric heaters can produce, thus costing you less money.

In the third paragraph of Section 22.3 (8th edition), there's a caveat that to be reversible, the gas must be able to return to its original state *without changing the surroundings*. Give an example of a process that would be considered reversible if not for that qualifier.

Pretty much any line that you can draw on a PV diagram would be reversible if not for that condition. Consider a constant volume change, a vertical line on a PV diagram. If the surroundings are hot, the gas will move up the line towards higher temperature. By making the surroundings cold, the gas will move down the exact same line, reversing its path.

The Carnot engine is completely impractical---because it has to operate reversibly, it would take it an infinite time to complete a cycle. (Even operating *almost* reversibly, it will take a long time to complete a cycle---it would still be impractical.) Why then do we bother? What is important about this engine?

The Carnot engine is impractical for use, but it's useful in comparing to other engines because it gives us an upper limit in efficiency. If your neighbor is trying to get you to invest in some new technology which gives an efficiency larger than the Carnot efficiency (something surpressed by the evil oil companies who want to keep the internal combustion engine reigning), you should do all you can to discourage them from throwing away their money.

Why doesn't the Carnot engine have perfect efficiency?

It exhausts some heat without converting it into work. Every engine must do this.