Chapter 4: Questions:

4. When water condenses from gas to liquid, or when water freezes, heat is released. In order to make ice, you must extract the heat from liquid water. This happens naturally if the temperature is already below freezing, or if the ambient temperature is above freezing, you need a refrigerator to pump heat out of the water into the environment.

9. Steam locomotives work by turning water into steam to drive the engine. There are two reasons a condenser (which converts the spent steam back into water) is needed.

1) The water can be reused
2) The engine is a heat engine which derives its energy from the high temperature of the incoming steam. This engine is more efficient if its exhaust is at lower temperature (more heat is turned into work), which the condenser accomplishes by cooling the steam into water.

Problems:

Problem 5. An electric tea kettle has an element which pumps heat into water at some fixed rate. A measure of this rate is that some amount of water is heated from 20 C to 100 C in 5 minutes.

We don't know the amount of water but it doesn't matter. What we do know is that it takes 80 calories of heat to raise the temperature of 1 gram of water by 80 C, and it takes 540 calories of heat to boil away 1 gram of water (at 100 C). Thus, it will take 540/80 (or 6.75) times 5 minutes to boil away all the water in the kettle, no matter how much is there! This is about 34 minutes.

CHECK THIS AT HOME if you don't believe it! Record the amount of time that it takes for a small pan of water on the stove to come to a boil from room temperature. It will take about 6.75 times as long to boil it away, no matter how much water was in the kettle.

Problem 8. A simple heat engine that makes use of warm air at 30º C (303 K) as a heat source and exhausts to a river at 10º C (283 K) would have an efficiency of (303 – 283) /303 x 100%, or 6.6%. What this means in practice is that a huge amount of heat has to be extracted from the air to get some useful work. Whether this would be cost effective is not clear.

This is similar to some practical proposals to extract heat from the ocean (at 27º C) and to use the ocean floor at 4º C as exhaust. The difference is that it is easier to extract heat from water than air, as air is very poor conductor of heat.

Problem 9. The theoretical maximum efficiency of any heat driven process is given by

Efficiency (%) = (Th - Tc)/ Th x 100% where Th is the temperature of the heat source and Tc is the temperature of the exhaust. Temperatures must be absolute (Kelvin).

For a steam plant that uses steam at 550 C and exhausts to the environment at 20 C

Th = 550 + 273 = 823 K, Tc = 20 + 273 = 293 K

Eff = (823 - 293) /823 x100% = 64%

If the plant actually operates at 38 %, this is 38/64 x 100% = 59% of the maximum possible, which is not too bad.

Problem 10. If an engine has 3000 Joules of heat added to it but 2200 come out in the exhaust, we would conclude that (3000-2200) got converted into useful work.

The efficiency is (work done)/(energy input) = 800/3000 x100% = 27 %

This is typical of an automobile engine. In this case the "heat added" is the fuel burning in the cylinder.

Dripping Faucet. The answer here depends on the drip rate. However, the energy required to heat 1 gallon (8 pounds) of water from 50º F to 120º F is 560 Btu or 0.164 kwh. (Use 1 kwh = 3413 Btu). If you want to work out cost, in Eugene this would be about $0.06 x 0.164 or about $0.01 / gallon. Nationally, it would be more expensive.

If a drip wastes 5 gallons/day, this would be about $1.50 per month.

Ch. 5

1. Add R-values for wall materials:

½ inch lapped siding:      0.81
½ inch plywood             0.62
½ inch sheetrock            0.45
3 ½ inch fiberglass        10.9
---------------------------------
Total                             12.8  then (1/12.8) times temp difference 50 F = 3.9 Btu/hr (per square foot of wall)

7. Room air conditioner removes 6000 Btu/hr of heat.

The wood shack is 10x10x6 ft with simple 1 inch softwood siding.

The walls have area = 4x60 square feet = 240 square feet.
The ceiling and floor have 2x100 square feet.
Total area = 440 square feet.

Softwood siding has R = 1.25

Total heat loss for (95 – 70 F) = 25 F temperature difference is

Q/t = (1/R) x A x delta T = (1/1.25) x 440 sq. ft. x 25 F = 8,800 Btu/hr.

This air conditioner is not enough to keep it cool. Insulate the shack!