Physics 140:
Greenhouse
Effect
Spring 2008
Homework #2 Solutions- Due Wednesday, February 20,2008
Each part of each problem is worth 2 points unless otherwise noted. In
all problems: give the units with the numerical answer (unless the
answer is a pure number). Round final answers to the appropriate number
of significant figures (one or so extra is ok). SHOW YOUR WORK for all
parts of all answers!
1) (a) (1 pt) What is the kinetic energy, in J, of a 130 lb person plus
a 20 lb bicycle traveling 10 miles per hour?
Answer:
10 miles/hour x 1600 m/mile x 1 hour/3600 s = 4.44 m/s
150 lb x 1 kg/2.2 lb = 68.2 kg
kinetic energy = (1/2)mv2 = 0.5 x 68.2 kg x (4.44 m/s)2
= 672 kg m2/s2 = 672 J
(b) By how much, in J, does the potential
energy of a 130 lb person plus a 20 lb bicycle increase when climbing a
200 ft hill?
Answer:
200 ft x 1 m/3.28 ft = 61.0 m
potential energy = mgh = 68.2 kg x 9.8 m/s2 x 61.0 m =
40,800 kg m2/s2 = 40,800 J
Convert this to food calories (1 food calorie = 1000
calories).
Answer:
40,800 J x 1 cal/4.184 J x 1 food calorie/1000 calories = 9.7 food
calories
If humans are 20% efficient at converting chemical energy to
mechanical energy, how many calories (out of a typical daily intake of
2000 calories) would climbing this hill burn?
Answer:
0.2 x input food calories = 9.7 food calories of useful energy
Solve to get input food calories = 49 food calories
2) The "power boil" burner on a current-model gas range has a heat
output of 15,000 Btu/hr. Convert this to W.
Answer:
15,000 Btu/hr x 1055 J/Btu x 1 hr/3600 s = 4,400 J/s = 4,400 W.
3) Search on the Internet for a report of a specific recent discovery
of new oil reserves. Attach a copy of the relevant page and circle or
highlight the estimated size of the new reserves, in barrels.
Using this figure, compute how long it would take to use up this new
supply, taking the world consumption rate as 80 million barrels per day.
Answer: Let's take, for example, the reported discovery in Brazil of a
new reserve of 5 to 8 billion barrels. Let's take the low number, 5
billion, and see how long it will last at the current rate of world
consumption.
5 billion barrels x 1 day / 80 million barrels = 62.5 days
(the high number, 8 billion, would last 100 days).
4) My solar panel has an area of 20 m2 and an
efficiency of 20%. If the sun shines directly on my panel with an
intensity of 700 W/m2, what is the power output?
Answer: Input power is 700 W/m2 x 20 m2 = 14,000
W. Use
input power x efficiency = output power
to compute 14,000 W x 0.20 = 2,800 W = 2.8 kW
5) The electrical energy generated in the US in 1999 was 3.2 trillion
kWh.
(a) What was the total average power output of US
power plants in 1999, in GW?
Answer:
3.2 trillion kWh / year x 1 year/(24 x 365) hrs = 0.000365 trillion kW
= 365 billion W = 365 GW
(b) (1 pt) If the demand for electrical energy were
to double, how many 1000 MW power plants would have to be built to
satisfy the additional demand?
Answer:
You need to produce another 365 GW of power.
365 GW = 365,000 MW = 365 x 1000 MW, so you need to build 365 power
plants/
(c) (1 pt) If this doubling were to happen between
1999 and 2020, how many 1000 MW power plants would have to built per
month?
Answer:
365 power plants / 21 years x 1 year/12 months = 1.4 power plants/month
(d) If all of these plants were powered by fossil
fuels, how much would fossil fuel energy consumption, in quads/yr, have
to increase from its 1999 value in order to double the electrical
energy output? Assume the average efficiency is 35%. Compare this
to the total fossil fuel
energy consumption of 81.6 quads in 1999.
Answer:
We will produce an extra 3.2 trillion kWh/yr = 3.2 trillion kWh/yr x
3.412 thousand Btu/kWh = 10.9 thousand trillion Btu/yr = 10.9 quads/yr.
With an efficiency of 35%, we have
0.35 x fossil fuel energy input = electrical energy output = 10.9 quads
Solve for fossil fuel energy input = 31 quads.
This is a substantial fraction (more than a third) of the total fossil
fuel energy consumption, and would have a significant impact on the
market and on carbon dioxide production.
(e) Search on the Internet for an article
describing the building of new power plants, either in the US or
abroad. Add up the total additional power, in GW, that will be provided
by the plants described. Attach a copy of the article with the power of
the power plants underlined or circled.
Useful information
1 kg = 2.2 lbs
1600 m = 1 mile
1 calorie = 4.184 J
1 m = 3.28 ft
g = 9.8 m/s2
1 Btu = 1055 J
Heat of fusion of water = 140 Btu/lb; heat of vaporization of water =
970 Btu/lb
1 kWh = 3412 Btu
1 quad = 1015 Btu