Goal: to understand Thermodynamics

Objectives:1) To learn the first law of Thermodynamics

2) To learn about the PV diagram3) To learn about work done on a gas

4) To learn about work at constant pressure5) To learn about work at a constant volume

6) To learn about work at a constant Temperature7) To learn about Adiabatic processes

8) To examine heat engines and heat pumps

First Law

• ΔU = Q + W

• U = internal energy

• Q = heat

• W = work done ON the gas

PV diagram

• Will show the starting Pressure and Volume of both the initial state and the final state.

• W = - Pave ΔV

Constant Pressure

• P = Pave

• So, W = -P ΔV

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

Constant Volume

• W = -P ΔV

• If ΔV = 0 then W = 0J

• So, ΔU = Q

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 won’t 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

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)?

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?

Adiabatic Process

• In this case there will be no heat flow.

• That is to say Q = 0

• So, W = ΔU = 1.5 nR ΔT

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?

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 ΔV for each step

• You add up the steps to get a net work

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 ΔV = 0J as V has not changed

Step 2

• You push in the piston out increasing the volume.

• W = -P ΔV 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.

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.

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.

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.

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.

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 < 1

Conclusion

• We have learned about heat engines

• We have learned about heat pumps/refrigerators

• We have learned about efficiency