Simple Nature - Light and Matter

numbers. With a purely numerical approach, we wouldn’t evenhave known what value of m to pick, or if we’d guessed a valuelike 1 kg, we wouldn’t have known whether our answer dependedon that guess.Solving for ∆T , and writing v instead of v i for simplicity, we find∆T = v 22c≈ 40 ◦ C .The passengers would be boiled alive if not for the refrigeration.The first stage of cooling happens via heat exchangers in theengine struts, but a second stage, using a refrigerator under thefloor of the cabin, is also necessary. Running this refrigeratoruses up energy, cutting into the fuel efficiency of the airplane,which is why typically only 50% of the cabin’s air is replaced ineach pumping cycle of 2-3 minutes. Although the airlines preferto emphasize that this is a much faster recirculation rate than inthe ventilation systems of most buildings, people are packed moretightly in an airplane.2.1.4 PowerPower, P , is defined as the rate of change of energy, dE/ dt.Power thus has units of joules per second, which are usually abbreviatedas watts, 1 W=1 J/s. Since energy is conserved, we wouldhave dE/ dt = 0 if E was the total energy of a closed system, andthat’s not very interesting. What’s usually more interesting to discussis either the power flowing in or out of an open system, or therate at which energy is being transformed from one form into another.The following is an example of energy flowing into an opensystem.Heating by a lightbulb example 4⊲ The electric company bills you for energy in units of kilowatthours(kilowatts multiplied by hours) rather than in SI units ofjoules. How many joules is a kilowatt-hour?⊲ 1 kilowatt-hour = (1 kW)(1 hour) = (1000 J/s)(3600 s) = 3.6 MJ.Now here’s an example of energy being transformed from oneform into another.Human wattage example 5⊲ Food contains chemical energy (discussed in more detail in section2.4), and for historical reasons, food energy is normally givenin non-SI units of Calories. One Calorie with a capital “C” equals1000 calories, and 1 calorie is defined as 4.18 J. A typical personconsumes 2000 Calories of food in a day, and converts nearly allof that directly to body heat. Compare the person’s heat productionto the rate of energy consumption of a 100-watt lightbulb.⊲ Strictly speaking, we can’t really compute the derivative dE/ dt,80 Chapter 2 Conservation of Energy