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The First Law of Thermodynamics and Heat TransferMaking Heat Work for You!
Oh, bother! It’s summer, again! I don’t like summer. Summer means going to the beach. And, for me, going to the beach means diet time. I have hibernated since Thanksgiving (in
November!) and now it’s time to pay for it. Basically, I have stored up a bunch of energy and
I need to get rid of it. Maybe science can help…
My body just doesn’t get it! I am in constant thermal contact with my
environment. Sometimes I’m in Thermal contact with air, now. Sometimes I’m in Thermal contact with water,
swimming. Sometimes I’m in Thermal contact with a mattress,
sleeping. In each case, my body is always 37°C.
But the air is 10°C at night and 30°C during the day. The water at the pool is about 25°C. The bed is about 20°C.
What does the 0th Law of Thermodynamics say about this?
My body just doesn’t get it! The 0th Law says that if there is a temperature
difference between me and something else, then we MUST exchange heat energy until our temperatures are the same.
But my body keeps plodding along at 37°C. So, I keep losing heat energy.
Now all this heat energy that I keep giving to the environment must be coming from somewhere…from my stored energy…my fat!
This is great!!! The 0th Law is on my side
Ok, Science! Don’t fail me now! So, I’m constantly losing weight (internal energy)
by just standing here! Amazing! No more silly diets! No more pointless
trips to the gym! Success! Now, I would like to lose 20 pounds of fat…
20 pounds is about 9000 grams. Each gram of fat is worth 9 food Calories 1 food Calorie is 1000 real calories 1 real calorie is 4.186 joules
So I need to lose 300,000,000 Joules or 300x106J or 300 MJ.
Ouch…
Ok, Science! Don’t fail me now! Ok, now I have until August 14th (Vacation!) to do this.
That is 54 days from now…about 5 million seconds or 5x106 s or 5Ms.
And I plan on eating…700MJ more… That means I need to average 1000 MJ / 5Ms…about
200 J/s This number, energy/time, is called power, P. The unit J/s is called a Watt, W. The 0th Law of Thermodynamics demands that I lose
heat to the objects I am in thermal contact with (because of temperature difference), but it doesn’t say how that happens…or, more importantly, how quickly that happens.
Three ways to transfer heat Conduction movement of heat through an
object Example: Touch a hot pan Power Equation:
Radiation movement of heat using Electromagnetic (EM) waves Example: Sun…anything actually Power Equation:
Convection movement of heat using a fluid Example: Hot air moving upward…creates weather Power Equation: …Maybe when you’re older…
L
TTkAP CH
Conduction
−=
4ATPRadiation σε=
Heat transfer example #1 What if I just stand here…What is my power
output from radiating heat? What is my net power exchange with my
environment?
Heat transfer example #2 Ok, radiating heat didn’t help, what about
conduction? Let me place my feet in ice water and see what happens.
Can we speed it up? It seems to me that I run into this problem every
summer. Unfortunately, the 0th Law could not save me. I’ve tried every crazy diet known to humankind. Only one rule has always worked Change in weight = Calories consumed – Calories spent Basically translated, to lose weight, eat less and
exercise more. This is actually a rewording of another
conservation law we already know… Conservation of Energy…It just keeps coming back, doesn’t
it?
1st Law of Thermodynamics Change in weight = Calories consumed – Calories spent In the case of Thermodynamics,
Change in weight = ∆EInternal , the change of the Internal Energy of the system
Calories consumed = Q , The energy added as heat energy to the system
Calories spent = W , the work done by the system ∆EInternal = Qadded to system – Wdone by the system
Or ∆EInt = Q – W Let’s examine this in terms of weight loss
Idea #1 I could consume 0 Calories. This is like adding 0 heat energy to my system,
Q = 0. In that case, ∆EInt = W In other words, whatever energy I spend doing
work (exercising) would come directly from my stored internal energy!
In physics this is called an Adiabatic Process
Idea #2 Over the last 7 months (Wow! Really! 7 months) I
have not exercised at all This is like doing no work…W = 0 In that case, ∆EInt = Q In other words, the energy I consume goes right
into my stored internal energy In physics, this is called a ConstantVolume
Process (I’ll explain why a little later)
Idea #3 Once I do figure out how to get to my proper
weight, I want to stay there This is like demanding that ∆EInt = 0 In that case, Q = W In other words, the energy I consume goes into
my exercise work In physics this is called a Cyclic Process
Idea #4 I could find my perfect weight, then not eat
anything or do any exercise. This is like demanding ∆EInt = 0 and Q = 0 and
W = 0 In that case, ∆EInt = 0, but I can’t do any work, W
because I haven’t added any heat, Q In other words, I’m completely motionless…like
on Sunday… In physics this is called a Free Expansion
Let’s examine each variable a little closer Heat added, Q …
It is negative if heat leaves the system It is positive if heat enters the system Q = mc∆T, or Q = mL, or …
The change in the internal energy, ∆EInt
Literally, ∆EInt is equal to EInt, f EInt, i
This behaves just like conservation of energy. It does NOT depend on the path, just the initial and
final points! The Work done by the system, W
It is positive if the system does work It is negative if work is done on the system
Finding work… Work is the difficult variable… We know Q from Friday, and ∆EInt from Phys 211
ideas, but how do we find W? Remember from Phys 211? Work is force * distance! How much work do I do when I lift weights? But if the force is changing…integrate…area! Area under the line!
Finding work…gas in a cylinder
Finding work…the pV diagram
W > 0
W < 0
Finding work…the pV diagram
W > 0
W > 0
Finding work…the pV diagram
Wexpansion > 0
Wcontraction < 0
Wnet > 0
Concept Test Time!
Consider the cycle above… Is ΔEInt positive, negative, or zero? Is W positive, negative, or zero? Is Q positive, negative, or zero?
I’m tired of graphs If we just knew how p and V are related we could
just do the integral mathematically Sometimes we do…ideal gas pV = nRT pV = NkT
Credits Images from Halliday, D., Resnick, R., & Walker,
J. (2008). Fundamentals of Physics (8th ed.). Danvers, MA: John Wiley & Sons, Inc.
Music by Rick Fouche Presentation by Gerardo Giordano