Whiteboarding!1. Form a group of 3 or 4 no more no less2. Collect a Whiteboard and pens, and work your way

through the following two problems3. Make sure you are contributing to your group, if you

are not then start a new group!

PV-DiagramsPressure/Volume graphs are of tremendous value in analyzing the performance of heat engines. Essentially, the amount of work produced by an engine depends on the path it takes (changes in pressure and volume)

PV-DiagramsConfused…? Expected, let’s start slow1. Engines follow a path, in

this case from 1 2, 23, 34, and 41

2. Each affects the Work done by, or done on the System

Net Work of a MachineLet’s study the engine to the right…Q: is the direction of the arrows important?

P

Vab

c

P1

P2

V1 V2

d

Net Work of a MachineLet’s study the engine to the right…Q: is the direction of the arrows important?

YES! Challenge is if work is done ON the system or BY the systemNote: Please write down the work done for each of the next four steps

P

Vab

c

P1

P2

V1 V2

d

Step 1: Process a b represents an isobaric compression of a gas

From a to b, the pressure remains constant – its value is P1. The volume decrease from V1 to V2. This represents work done on the system. How can you calculate the W?

P

Va1P

V1 V2

b

Step 1: Process a b represents an isobaric compression of a gas

From a to b, the pressure remains constant – its value is P1. The volume decrease from V1 to V2. This represents work done on the system. How can you calculate the W?

P

Va1P

V1 V2

b

Step 2: Process b c is an isochoric compression

Isochoric because the volume does not change but the pressure increases. What is the work for this step?

ZERO!!!

P

Vb

c

P1

P2

V1

Step 3: Process c d is an isobaric expansion.

The gas expands from V1 to V2, doing work as it expands. The amount of work is equal to the area under the curve.

P

V

c d2P

V1 V2

Step 4: Process d a is an isochoric expansion

Volume stays constant. So no work is done. Pressure decreases.

P

Vab

c

P1

P2

V1 V2

d

Complete CycleBased on what you have recorded for the work on each step, what is the total work done on the system?

P

Vab

c

P1

P2

V1 V2

d

Complete CycleBased on what you have recorded for the work on each step, what is the total work done on the system?

OR just the area of the enclosed area!

P

Vab

c

P1

P2

V1 V2

d

Overall

Question 1:A substance undergoes a cyclic process shown in the graph. Heat transfer occurs during each process in the cycle. (a) What is the work output

during process a b? (b) How much work input is

required during process b c?

(c) What is the net work done during the cycle

Note: 1 atm = 1.013 x 105 PaNote: 1 L = 0.001 m3

P (atm)

V (L )

a

bc1.00

5.00

10.0 50.0

Question 1:A substance undergoes a cyclic process shown in the graph. Heat transfer occurs during each process in the cycle. (a) -1.22 x 104 J (Expansion

process, so work is done on surroundings)

(b) 4.05 x 103 J (c) -8.15 x 103 J

P (atm)

V (L )

a

bc1.00

5.00

10.0 50.0

Question 1:

Question 2:A heat engine’s cycle is shown in the PV diagram to the right.

P1 = 345 kPa, P2 = 245 kPa, P3 = 125 k Pa, and P4 = 225 kPa. V1 = 35.0 L and V2 = 85.0 L. What is the net work done during one cycle of the engine?Note: 1 L = 0.001 m3

P

V

ab

cd

P1P

4P2

P3

V1 V2

Question 2:A heat engine’s cycle is shown in the PV diagram to the right.

P1 = 345 kPa, P2 = 245 kPa, P3 = 125 k Pa, and P4 = 225 kPa. V1 = 35.0 L and V2 = 85.0 L. What is the net work done during one cycle of the engine?Note: 1 L = 0.001 m3

Ans: -6.00 kJ

P

V

ab

cd

P1P

4P2

P3

V1 V2

Question 2:

1st Law + Carnot Cycle – An Ideal Engine

1. Please put away the whiteboards 2. Collect the 1st Law Up to Now Worksheet + the

handout on the Carnot Cycle, make sure to read this!

3. By now you should have complete most of the MC questions from the Thermo Package

4. We will have our last quiz in 20 minutes!

1st Law incomplete• Conservation of Energy, however processes that do

conserve energy, still don’t appear to happen! WHY!?

A coffee cup breaks spontaneously but is unable to get put back together spontaneously

Clausius statement: “it is impossible for a self acting machine working in a cyclic process without any

external force, to transfer heat from a body at a lower temperature to a body at a higher temperature.”

Engine Efficiency “Engine Statement”It is impossible for any system to undergo a process in which it absorbs heat from a reservoir at a single temperature and converts the heat completely into mechanical work, with the system ending in the same state in which it begins.

Workless Refrigerator

“Refrigerator Statement”:It is impossible for any process to have as its sole results the transfer of heat from a cooler to a hotter body

2nd Law of Thermodynamics

Efficiency ≠ 100%The Carnot Cycle represents the MAXIMUM efficiency for a heat engine

1. Isothermal exp.2. Adiabatic exp.3. Isothermal comp.4. Adiabatic comp.

Derivation

Efficiency of Carnot Cycle

Quiz! ~ Heat EnginesPlease set up for 4th and final quiz

More Handouts!• Download the AP Thermodynamics Wrap-up that reviews

all the equations and how the work… VERY USEFUL!• Next Class: Thermo Unit Test

Let’s Review! Take out your phones and/or computers and log onto Socrative.Room Number: Slawson