## Power

In which we find out the difference between ...

power vs. energy.

If a 70 kg hiker and a 70 kg Tour de France racer climb the same distance, have they gained the same amount of gravitational potential energy? or a different amount?

What's different between the two groups?

Bring in cup, gallon container, and talk about difference between flow rate and volume of water. If you have a flow rate of 1 gallon / 3 sec, how much water (how much volume) is deposited in 1 second? in 6 seconds? in one minute?

### The quickness of energy transformation

The notion that captures this idea of how quickly work is done is...

Power = $\frac{W}{t}$ = work done / time to do it=$\frac{E}{t}$ = energy/time

SI Units 1 Joule / sec $\equiv$ 1 "watt"

Remember our comparison of the energy/gram of TNT (0.65 Cal / g) vs chocolate chip (5.0 Cal / g)? But, the energy in TNT can be released much, much faster (energy / time) than the energy in a chocolate chip cookie.

### Student power

In the student power exercise, you will climb a height $h$ equal to
$h =$ (number of steps) $\times$ (height of one step [cm]) $\times \frac{\rm 1\ m}{\rm 100\ cm}$.

Your mass is... $m$ [kg] = (weight [lbs]) $\times \frac{\rm 1\ kg}{\rm 2.2\ lbs}$.

Estimate in class before they do it...

The total gravitational energy you gained was...
GravE = $m\cdot g\cdot h=$(your mass [kg]) $\times$ 9.8 m/s${}^2 \times$ (height [m]) = _____ Joules

So your power = energy / time is:
power = (GravE [J]) / (time [sec]) = _____ Watts

### Light Bulb

How many light bulbs could you keep going???

100 W=100 J/s for an incandescent, '100 W' bulb.

Only About 2% of the incoming ElectricE comes out as light, 98% is heat.

#### Luminous efficiency

In general, efficiency is: $$\frac{\text{energy in some useful form}}{\text{total energy input}}.$$

 candle 0.04% incandescent 2% compact fl. 10% LED (theory) 40%

2010: A european ban on selling incandescent light bulbs has gone into effect. They want citizens to buy compact fluorescents or LED fixtures which have a much higher efficiency. But a german businessman is trying to get around the ban by selling incandescents labelled as "heat balls".

### Tour de France racers

Stage 1 time trial, 2005 Tour de France, 19 km, only 20 m of climbing (it was "flat")

Floyd Landis placed 6th in 21 m 53 s
Average Speed: 32.3 mph (52.1 km/h)
Estimated Total Work (energy): 582 Kjoules
Cycling power.

Time = 21 min 53 sec/
How many seconds is that?

Work = 582 Kjoules.

How many Joules is that?

Power = Work / time
What was his average power?

### Average athletes

More typical figures for non-elite athletes: Vigorous, but sustained exercise is output of ~ 100 W = 100 J/s for sustained periods.

How many Joules of energy do you use while playing frisbee for 1/2 hour?...

Power (J/s) = energy / time. So, if you have power and time... how do you figure the energy?

half an hour = how many seconds?

So, how many Joules are you expending to play for 1/2 hour?

Now, it turns out that the human body is ~25% efficiency: you must eat 4 Calories for every 1 Calorie you expend. So... how many Joules of food energy do you need to eat to exercise for 1/2 hour?

But usually we talk about Calories, not Joules. What's the connection?

### Heating water

What's a calorie? [little c]

1 cal is the amount of heat (thermal energy) needed to raise 1 ml of water by 1 degree celsius.

How many ml (milli-liters) in 1.5 liters?

How many calories needed to raise the temperature of 1.5 liters of water by 75 C?

1 cal = 4.187 J

How many Joules needed to heat 1.5 liters up by 75 C?

This electric kettle says '1500 watts' =1.5 kW=1500 J / s

1500 watts is also typical of a microwave oven.

How long does it take to boil 1.5 L of water at 1500 watts, starting at room temperature (25 C) $\to$ boiling (100 C)?
Start with Power = $\frac{E}{time}$, so what's the time, given the power and energy needed?

### Calories in food

One "Calorie" on a food label is actually 1 kilocalorie in terms of our thermal definition.

1 "Calorie" = 1 kcal = $10^3$ calories = 4187 J

Humans require about 12 Cal of food / lb / day. How many calories/day for a person weighing 150 lbs?

So, 170 Calorie is what percent of your daily energy needs?

This is about the same as the number of Calories (165) in a 12-oz can of Mountain Dew.

So, the number of Calories you use, just sitting around in one day....

 = / per day

Some dieticians try topoint out the difference by writing food Calories with a capital "C". But it's better just to know this from context. Anytime you hear "food" you know that what they *really* mean is kilocalories.

### back to Exercise

1/2 hr vigorous exercise requires ~ 700,000 J $\times$ 1 Cal/4200 J = 167 Cal $\approx$

1/2 hr =

### Losing weight

How many Calories do we have to burn to lose 1 lb?

1 lb (~450 g) of butter has about the same number of Calories as 1 lb of body fat: 3200 Cal.

To lose 1 lb / week, you'd need to either

• reduce your Calorie intake by about 3200/7 ~ 450 Cal each day $\approx$
• Or you could exercise more: about how much *more* exercise would do it?

### Electric usage

Power = E/t $\to$ Energy = Power * time.