Goal: to understand Thermodynamics

1
Goal to understand Thermodynamics

• Objectives
• To learn the first law of Thermodynamics
• To learn about the PV diagram
• To learn about work done on a gas
• To learn about work at constant pressure
• To learn about work at a constant volume
• To learn about work at a constant Temperature
• To learn about Adiabatic processes
• To examine heat engines and heat pumps

2
First Law

• ?U Q W
• U internal energy
• Q heat
• W work done ON the gas

3
PV diagram

• Will show the starting Pressure and Volume of
  both the initial state and the final state.
• W - Pave ?V

4
Constant Pressure

• P Pave
• So, W -P ?V

5
Sample

• A air filled balloon is placed inside a freezer
  by mistake. The balloon shrinks from a volume of
  0.004 cubic meters to 0.003 cubic meters.
• If the air pressure remains a constant 1.0 105
  Pa then find the work done ON the balloon

6
Constant Volume

• W -P ?V
• If ?V 0 then W 0J
• So, ?U Q

7
Constant Temperature

• In this case there will be no change in internal
  energy (U 1.5 kT)
• So, Q W 0 or, W -Q
• Using fancy math I wont replicate it turns out
  that you will get that
• W nRT ln(Vi/Vf)
• R gas constant 8.314 J/(mol K)
• n of moles

8
Example

• A balloon is attached to a rock and tossed into
  an ocean which has the same temperature as the
  air.
• The balloon sinks to a depth of 10 m at which
  point the outside pressure has doubled.
• As a result before we get into the problem
  what will happen to the balloon (hint thing net
  force)?

9
Example continued

• A balloon is attached to a rock and tossed into
  an ocean.
• The balloon sinks to a depth of 10 m at which
  point the outside pressure has doubled.
• You now know what will happen to the volume (that
  is to say the value of Vi/Vf)
• In this particular balloon there were 200 moles
  of an ideal gas.
• What will the work done on the balloon be?

10
Adiabatic Process

• In this case there will be no heat flow.
• That is to say Q 0
• So, W ?U 1.5 nR ?T

11
Example

• The balloon from the previous example is cut from
  the rock tied to it and can now shoot upward very
  quickly.
• What is the work done on the balloon if it does
  not have time to exchange any heat?

12
Heat Engines

• Takes energy in some form and coverts it to heat
  so that you can transform the energy to what you
  want/need.
• They process in a cycle such that you get a net
  work out of it.
• That is W -P ?V for each step
• You add up the steps to get a net work

13
Combustion Engine

• Is one form of engine
• You have a piston in a chamber that changes the
  size of the chamber
• Step 1
• You start with a small volume and up the
  temperature to create a large pressure.
• W -P ?V 0J as V has not changed

14
Step 2

• You push in the piston out increasing the volume.
  
• W -P ?V since V drops this will be a negative
  work done ON THE GAS
• Which means positive work done on the piston.
• Step 3 push out the gas, which has a lower
  pressure than before so the change in volume will
  produce little work.

15
Step 4

• Piston pulled back out at a constant pressure.
  This negates step 3.
• Final step piston goes back in to recompress the
  gas. However it is done at a lower pressure so
  the work done in this step is far lower than the
  work done in step 2 so the net is that work is
  done on the piston, and therefore the car.

16
Efficiency

• E Wnet / Qused
• This just tells you what fraction of the energy
  is used for what you want. The rest is wasted
  as exhaust, ect.

17
Heat Pumps / Refrigerators

• Work in the reverse
• They try to exhaust MORE heat.
• You compress a fluid. This heats it.
• That heat is then radiated or pumped via a fan
  outside the system.

18
Efficiency

• Is usually greater than 1 (many are 9 to 10)
• The reason, you are using a little bit of energy
  to toss out a LOT of energy.
• In other words you are just moving heat around.

19
Temperature difference reversible engine

• How cold you get the fridge is found by
• e 1 (Tc / Th)
• Tc and Th must be done in Kelvin
• Only works for e lt 1

20
Conclusion

• We have learned about heat engines
• We have learned about heat pumps/refrigerators
• We have learned about efficiency