AP Physics – 1 st Law Continued 1.Collect and read the handout on Heat Engine Efficiency from the front of the room 2.When finished work your way through the worksheet provided 3.In 20 minutes, we will explore PV diagrams and the Carnot Cycle 4.Next Class: The 2 nd Law of Thermodynamics

PV-Diagrams Pressure/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-Diagrams Confused…? Expected, let’s start slow 1.Engines follow a path, in this case from 1  2, 2  3, 3  4, and 4  1 2.Each affects the Work done by, or done on the System

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

Net Work of a Machine Let’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 system Note: Please write down the work done for each of the next for steps

Step 1: Process a  b represents an isobaric compression of a gas From a to b, the pressure remains constant – its value is P 1. The volume decrease from V 1 to V 2. This represents work done on the system. How can you calculate the W?

Step 1: Process a  b represents an isobaric compression of a gas From a to b, the pressure remains constant – its value is P 1. The volume decrease from V 1 to V 2. This represents work done on the system. How can you calculate the W?

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? 0!!!

Step 3: Process c  d is an isobaric expansion. The gas expands from V 1 to V 2, doing work as it expands. The amount of work is equal to the area under the curve.

Step 4: Process d  a is an isochoric expansion Volume stays constant. So no work is done. Pressure decreases.

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

Complete Cycle Based 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!

Whiteboarding! 1.Form a group of 3 or 4 no more no less 2.Collect a Whiteboard and pens, and work your way through the following two problems 3.Make sure you are contributing to your group, if you are not then start a new group!

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 = x 10 5 Pa Note: 1 L = m -3

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 10 4 J (Expansion process, so work is done on surroundings) (b)-4.05 x 10 3 J (c)-8.15 x 10 3 J

Question 1:

Question 2: A heat engine’s cycle is shown in the PV diagram to the right. P 1 = 345 kPa, P 2 = 245 kPa, P 3 = 125 k Pa, and P 4 = 225 kPa. V 1 = 35.0 L and V 2 = 85.0 L. What is the net work done during one cycle of the engine? Note: 1 L = m 3

Question 2: A heat engine’s cycle is shown in the PV diagram to the right. P 1 = 345 kPa, P 2 = 245 kPa, P 3 = 125 k Pa, and P 4 = 225 kPa. V 1 = 35.0 L and V 2 = 85.0 L. What is the net work done during one cycle of the engine? Note: 1 L = m 3 Ans: 6.00 kJ

Question 2:

1 st Law + Carnot Cycle – An Ideal Engine 1.Please put away the whiteboards 2.Collect the 1 st 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!

1 st 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

2 nd 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.

Efficiency of Carnot Cycle

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

More Handouts! Please collect three more handouts on Efficiency of Engines, the Second Law and… AP Thermodynamics Wrap-up that reviews all the equations and how the work… VERY USEFUL! Next Class: Thermo Unit Test AP Physics Tutorial: Next Tuesday Morning at 7:30-8:15 AM Please bring questions! If you’re at home we will be doing a Socrative Review! Please log in and take it!