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Read this through at home before you start!
There are two experiments described below, along with questions you should answer about each experiment. Part of each experiment requires making observations in "class" (either outside or in the downstairs lab) and this will be indicated. Because your time is limited, you should do this part for all experiments first. Interpret the experimental results and do the required calculations later. In special cases, students can check out some of the equipment so that if time does not permit to do all the work in the period allocated, some of the work could be done at home (for example, the stair climbing experiment).
Remember that energy can be precisely defined as the capacity to do work. Work, in turn, is defined as a force applied over a distance (in the same direction!). Doing work on something, or having it do work on something else, changes its total energy. With these definitions of energy and work we can compare many different forms of energy to one another and also to their equivalent in heat.
One generic form of energy is potential energy. Something with potential energy has the potential to have work done on it by the Earth's gravity. A very common type of potential energy, owing to the attraction due to gravity, is gravitational potential energy (or GPE). If you lift a book off a table, you do work on it and give it GPE. The GPE of an object is given by:
GPE = m g h (units: N-m)
g = 9.8 m/s2
where m is the object's mass (kg), g is the acceleration due to gravity (m/s2, constant near the earth's surface) and h is the height (m) of the object above its starting point. Letting go of the book allows the earth to do work on it, converting GPE into kinetic energy (KE), which is energy in motion. An object's kinetic energy is:
KE = 1/2 mv2 (units: N-m)
where v is velocity (m/s) and m is the mass, as before. Conservation of energy says that when the book falls, KE (gained) = GPE (lost).
Experiment 1: What is your power output in watts and horsepower?
Introduction:
Power is the rate of energy conversion (or consumption), which includes the rate of doing work:
Power = work done (Joules) /time to do it (seconds)
Think of a device's power rating as the upper limit on how much energy it can convert in a given time. The unit of power in the metric system is the watt (W). Energy is converted at a rate of one watt if one joule (J) is converted per second (units of J are N-m or kg m2/s2).
Do in class
Part I: Determine how many horsepower (watts, kilowatts) you can generate!
Run up a flight of stairs and have someone time you with a stopwatch. Try this again in a few minutes after resting to see how accurately the measurement can be repeated.
Measure the vertical height of the stairs in meters, that is, how much higher are your feet at the top of the stairs than at the bottom?
In running up the stairs, you have gained gravitational potential energy equal to your weight in Newtons (N = kg m/s2) (remember to use g=9.8 m/s2 times the height of the stairs in meters. In quickly running up the stairs, you expend energy to match this gain in potential energy. Your rate of gain of energy, or power is (change in energy)/(time to change).
Height of stairs (m)
Time to run up (sec) (sec) (avg)
Your weigh (in Kg) x 9.8 m/s2 = (N)
(1) What is your power output in watts and horsepower?
_____________ watts
_____________ hp (watts/746)
(2) Prove that you can be regarded as the energy equivalent of a 100 watt light bulb.
(Recall the movie The Matrix!) A human being must take in about 2500 Cal (food calories, or kilocalories) of energy in his or her food each day in order to continue to function normally. This means that he or she converts food energy to work and heat at a rate of (power) of 2500 kilocalories/day.
Using the fact that (1 calorie = 4.18 joules
or 1 Cal = 4180 joules), and the appropriate time conversions prove that
this rate of energy conversion is roughly the same as a 100 watt light bulb.
(Hint, convert total Cal to total joules and find the number of seconds in
a day).
Compare this result to the answer in Part (1) above. Why are they different?
(3) Compare with published values!
In a book we found a table (below) that lists the rate of energy use by a human being during various activities, but it is given in terms of body weight! It makes sense that activities like climbing stairs should depend on your weight, but can you trust the published values? In particular, what assumptions did the author make in listing the energy consumption as a result of these activities?
Table 1. Estimated energy expenditure rate for various activities in Cal/hr per N of body weight.
Sleeping 0.10
Walking (1.7
km/h) 0.34
Sitting still 0.13
Carpentry, plumbing 0.39
Standing relaxed 0.16 Active
exercise 0.43
Sewing by hand 0.17 Walking
fast (2.4 km/h) 0.45
Dressing, undressing 0.18 Going down steps 0.51
Singing 0.19
Loading heavy objects
0.56
Typewriting 0.20
Heavy exercise 0.62
Washing dishes 0.21
Tennis, swimming 0.73
Sweeping 0.22
Running (3.3 km/h) 0.84
Light exercise 0.28
Very heavy exercise 0.90
Going up stairs 1.50
From this table use the value for going up stairs and calculate your power output in Cal/hour (1.5 times your weight in Newtons). Convert this to watts and horsepower. How does this compare to the power rating you measured in Part (1)? Do you think that the power rating in the last line of the table is for walking or running up stairs?
Part 2. Energy content of fossil fuels
The energy content of fossil fuels is measured in terms of the heat liberated when the fuel is burned in air as cleanly as possible (that is, to carbon dioxide and other gases, no soot or particles, or to partially burned products such as carbon monoxide, which is a poison). In the United States, the Btu is the usual measure of energy content. This is the energy required to increase the temperature of 1 pound of water by 1 degree Fahrenheit. Thus, to bring 1 pound of water from room temperature (72 F) to boiling (212 F) requires 140 Btu. The rest of the world uses the calorie: the energy required to heat 1 g water by 1C.
In this experiment, we will carefully weigh some fuel (candle wax, lamp oil or methyl alcohol) in a burner and use this to heat up some water in a tin can. We will measure the rise in the temperature of the water, the amount of water (by weight) and the amount of fuel burned to get an idea of how much energy is available in a given fuel by weight.
The experiment is simple to do, but there are several unit conversions you must make in order to compare the answer you get with published or standard values. However, if you do the basic experiment accurately (regardless of the units that you choose to use), you can easily determine how much energy is available in just about anything that can be burned! For example, old rags, animal dung, wood of various moisture contents, oil and gas are used as fuel for heating around the world. How do these sources compare in terms of energy per unit weight or unit volume?
There will be various setups with candles, thermometers, metal cans or beakers and stopwatches (we want to know power, or rate of energy generation as well). We will use metric units in class (calories, grams, C) and convert these units at home.
For two different fuels:
Weigh and set up a can with about 500 grams (500 ml, about 1 cup) of water from the tap at about room temperature (20 C) in a "ring stand"- a metal stand with a holder for the can so that it can be suspended above a flame.
1. Carefully weigh an empty can and the can with water to the nearest 0.1 gram. (The can will absorb some heat but not nearly as much as the water, and we need to know how much water there is). There are two scales, one can measure relatively heavy objects, the other is for accurate measurements of lighter objects. Make sure the digital scale you use is set to zero before you start (tared), and air currents are not affecting it. Write these numbers down in the following table.
2. Carefully weigh a candle (in a metal cup to hold in wax, if it drips) or a small lamp (oil, or methanol) to the nearest 0.01 gram.
3. Mount the can and the candle or lamp on the stand.
4. Light the candle or lamp, start timing and quickly adjust the height of the can so that the flame just touches the bottom of the can. Arrange a cardboard windscreen around the can so that air currents don't disturb the measurement.
5. When the can has changed in temperature by a few degrees (5-10 C) blow out the candle or lamp gently so you don't blow wax or oil around.
6. Be sure to stir the water while measuring the temperature!
7. Let the candle or lamp cool and weigh it to the nearest 0.01 gram.
| Fuel 1 = | Fuel 2 = | |
| Weight of can + water | ||
| Weight of can | ||
| Weight of water | ||
| Weight of fuel+container (start) | ||
| Weight of fuel+container (end) | ||
| Weight of fuel burned | ||
| Water temp in C (start) | ||
| Water temp in C (end) | ||
| time to burn fuel (seconds) |
Things to consider: Does the can lose a significant amount heat to the room air while it is being heated? Check this by letting the can sit for a few minutes with the thermometer in it and note the cooling rate. Comments on cooling rate:
Repeat the experiment with a different fuel.
Do at home
The metric unit of energy as heat is the calorie, which is the amount of energy required to heat 1 gram (1 ml, 1 cubic centimeter) of water 1C.
1. Calculate the energy content of the fuel in calories per gram
To calculate heat energy absorbed by water in calories:
Total calories = number of grams of water x temperature rise in degrees.
If you had 500 grams of water in the can and its temperature increased by 5 C, this would mean 2500 calories of energy was absorbed by the water.
To calculate heat energy in calories produced by one gram of the fuel
Heat energy released per gram = Total heat absorbed by water / (grams of fuel)
If 0.5 grams of wax was burned, the energy released from the wax was 2500/0.5 = 5000 cal/gram.
If you can find the energy content of these fuels in calories per gram, great! Compare your values with the published values.
| Fuel 1 = | Fuel 2 = | |
| Energy Content (cal/g) | ||
| Published value (cal/g) |
Things to consider:
1) Liquid fuels like lamp oil are measured by volume (gallons, liters) and not by weight.
For water, 1 gram = 1 milliliter (1 ml). This is not true for liquid fuels!
As a first approximation, we can assume that the weight to volume relationship of oil and paraffin is the same as water (for water, 1 gram=1 milliliter (ml) so 1000 grams = 1 liter),
If you want to be more accurate you can look up the conversion of weight to volume (oil and paraffin is a bit lighter than water, so 1 gram takes up a bit more space than 1 ml). However, for wax, methanol and liquid fossil fuels, the conversion is approximately 0.9 grams = 1 ml fuel. This means 900 grams ~ 1 liter.
Note: 1 million cubic centimeters = 1000 liters or 1 metric ton of water.
Homework
1. For liquid fuels, convert the energy content of the fuel in calories per gram into Btu/gallon.
2. Compare your answer with the published figures, if you can find them.
For gasoline the energy content is usually given as 1.24 x 105 Btu per gallon (Hinrichs, Appendix B).
For most liquid fuels, your answer should be within about 50% or so of that for gasoline (between about 1.0 and 1.4 x 105 Btu/gallon) if you were careful! Show your work!
| Fuel 1 = | Fuel 2 = | |
| Energy content (Btu/gal) | ||
| Published value (Btu/gal) |
3. What is the power output of the candle or lamp in watts? (Expect an answer between 10 and 50 watts).
4. What would you do to improve the accuracy of this experiment? How much heat is not transferred from the flame to the can but instead escapes into the air?
Additional considerations (extra credit):
The metal in the can absorbs heat too, but not nearly as much by weight as the water does so you can ignore it as a first approximation. However, that can be taken into account. Look up the heat capacity of iron and water. The ratio of these two is the correction factor to convert the weight of the can into an equivalent weight of water. The heat capacity of iron is approximately 1/10th that of water.
To correct for this exactly:
Equivalent weight of water = weight of can x (heat capacity of iron)/(heat capacity of water).
Add the equivalent weight of water to the actual weight of the water to correct for the heat absorbed by the can. How much difference does this make for your answer? Does it give a better estimate for the heat content of the fuel (compared to published values) or does it make things worse>?
Energy and power conversions
1 Btu=252 cal.
1 joule = 4.184 cal
1 Cal (Food calorie) = 1 kilocalorie = 1000 cal
1 watt = 1 joule/second
1 horsepower = 746 watts