The first law of thermodynamics. U = internal energy. Q = amount of heat energy transfer

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1 Thermodynamics Investigation of the energy transfer by heat and work and how natural systems behave (Q) Heat transfer of energy due to temp differences. (W) Work transfer of energy through mechanical means. 1

2 The first law of thermodynamics U = internal energy Q = amount of heat energy transfer 2

3 W = amount of work causing energy transfer 3

4 Ex: A cylinder with a movable piston filled with a gas, compressed and heated at same time 4

5 VERY IMPORTANT Note1: When is ΔU = 0? Note 2: W on = W by 5

6 Those who breathe air, do this problem 1.) 2500 J of heat is added to a system and 1800 J of work is done on the system. (a) What is the change in internal energy of the system. (b) What would the internal energy change be if 2500 J of heat was added and the system did 1800 J of work as output (done BY system). 6

7 Concept Question A gas at an initial state with a temperature of 100 o C is brought to a final state of 150 o C. Must there have been heat flow into the system, out of the system, or neither. 7

8 PV diagrams Any Point on the diagram is a different "state" of the gas State = The gas is moved through these states through processes involving heat and work Where is the temperature??? P state 2 state 3 Where is the Work??? state 1 V How is /\U related 8

9 Special Types of processes 1. Isothermal 2. Adiabatic 3. Isobaric 4. Isochoric (Isovolumetric) 9

10 Isothermal Process Isothermal PV Diagram P V 10

11 Adiabatic Process. P V P V 11

12 Isobaric P V Isochoric (isovolumetric) P V 12

13 Key Summary Points For Special Processes 13

14 Concept Question For a given volume change, is more work done in an adiabatic or isothermal expansion. P V 14

15 HANDOUT Tips to Solving PV and Thermo Problems 1.) ΔU = Q + W on for ideal or almost ideal gases 2.) ΔU, Q and W on can be found by knowing two and finding the other. But they can also be found independently U = 3/2 n R T ΔU = 3/2 n R T f 3/2 n R T i W on = P ΔV = area under the curve (+W for ΔV, W for ΔV +) 3.) PV = nrt can also be used 4.) Be aware when ΔU, Q and W are zero Q = 0 W = 0 Adiabatic process Isochoric process or if you go back and forth so that you have W in one direction and an equal + work in the other ΔU = 0 Isothermal process Also ΔU = 0 if you return to the same point on the process. Each pt on the PV curve represents a certain temp, if you go back to the same point you will be back at the same initial temp so ΔU = 0 15

16 2.) A gas expands from an initial volume of 0.40 m 3 to a final volume of 0.62 m 3 at the pressure increases linearly from 110 kpa to 230 kpa. Find the work done by the gas. P V 16

17 3.) An ideal gas expands isothermally, performing 4.4x10 3 J of work in the process. Calculate the change in internal energy of the gas and the heat absorbed during the procesṡ 4.) Sketch a PV diagram of the following process and label each part of the process accordingly: 2 L of ideal gas at atmospheric pressure are cooled at constant pressure to a volume of 1 L, and then expanded isothermally back to 2 L, whereupon the pressure is increased at constant volume until the original pressure is reached. P V 5.) 1 L of air initially at 6.5 atm of absolute pressure is allowed to expand isothermally until the pressure is 1 atm. It is then compressed at constant pressure pressure to its initial volume. Finally, it is brought back to its original pressure by heating at constant volume. Draw the process on a PV diagram and label each section accordingly. P V 17

18 6.) In an engine, an almost ideal gas is compressed adiabatically to half its volume. In doing so, 1350 J of work is done on the gas. (a) How much heat flows into or out of the gas (b) What is the change in internal energy of the gas (c) Does its temperature rise or fall. (d) assuming the initial temperature of the gas was 300 K and there was 1 mol, determine the final temperature of the gas (e) in terms of V o (the initial volume of the gas) determine the pressure difference from the beginning to end of this process P V 18

19 7.) An ideal gas is slowly compressed at a constant pressure of 2 atm from 10 L to 2 L. Heat flows out and the temperature drops during this process. Heat is then added to the gas, holding the volume constant and the pressure and temperature are then allowed to rise until the temperature reaches its original value. (a) Sketch a PV diagram of the two processes and name each accordingly. (b) Calculate the total work done by the gas (c) Calculate the total heat flow into the gas P V 19

20 8.) 2004B5. (10 points) The diagram above of pressure P versus volume V shows the expansion of 2.0 moles of a monatomic ideal gas from state A to state B. As shown in the diagram, P a = P b = 600 N/m 2, V a = 3 m 3, and V b = 9 m 3 (a) i. Calculate the work done by the gas as it expands. ii. Calculate the change in internal energy of the gas as it expands. iii. Calculate the heat added to or removed from the gas during this expansion. (b) The pressure is then reduced to 200 N/m 2 without changing the volume as the gas is taken from state B to state C. Label state C on th diagram and draw a line or curve to represent the process from state B to state C. (c) The gas is then compressed isothermally back to state A. i. Draw a line or curve on the diagram to represent this process. ii. Is heat added to or removed from the gas during this isothermal compression? added to removed from Justify your answer. 20

21 9.) When a gas is taken from a to c along the curved path; the work done is 35 J and the heat removed from the gas is 63 J. Along path abc, the work done is 48J. (a) What is Q for path abc? b a c d 21

22 Third, Second Law and Heat Engines 3 rd Law absolute zero is impossible (a conclusion resulting from the second law and ideas about entropy approaching zero) 2 nd law of Thermodynamics A law of nature s constraints in thermodynamic systems (heat engines, refridgerators, etc.) and a general statement of the natural processes in the world (energy dissipation) a) Clausius Statement aka: entropy b) Kelvin Planck statement c) Entropy 22

Entropy Ice Melting Analogy Universe = Room + Ice Water System Room 'surroundings' 27 o C (300K) heat flow Heat leaves the Room 'surroundings' and flows into ice 1000 J Ice Water 'system' 0 o C

23 Entropy Ice Melting Analogy Universe = Room + Ice Water System Room 'surroundings' 27 o C (300K) heat flow Heat leaves the Room 'surroundings' and flows into ice 1000 J Ice Water 'system' 0 o C (273K) Decreasing Entropy ΔS r = - Q / T ΔS r = / 300 ΔS r = J/K Heat flows into the ice-water system (energy disperses in that system) Increasing Entropy ΔS i = Q / T ΔS i = 1000 / 273 ΔS i = 3.66 J/K Overall in total the entropy of the 'universe' has increased as it always does 23

24 HOW ENGINES WORK 24

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through converting chemical energy into thermal energy, d) expand the combustion products, and then (STROKE 3

26 Four Stroke Internal Combustion Engine The Otto Cycle (4 stroke engine) 5 steps to the process a) ingest a mixture of fuel and air, (STROKE 1 INTAKE) b) compress it, (STROKE 2 COMPRESSION) c) ignite it, adding heat through converting chemical energy into thermal energy, d) expand the combustion products, and then (STROKE 3 POWER) e) eject the combustion products and repeat back to (a) (STROKE 4 EXHAUST) 26

27 Inline Vee advantage (space saving) FLAT (Boxer) ex:porsche 27

28 Thermodynamics Of Heat Engines 28

29 Efficiency Rate of heat gain or loss / and Power. 29

30 Heat Engine PV Cycle (Otto Cycle) 30

31 Heat Engine PV Cycle (Otto Cycle) ,

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33 Carnot efficiency the theoretical maximum an engine can operate at with no losses (different for different engines, and much less than 100% which it even theoretically unattainable based on the 2nd law) An idealized carnot engine is called a reversible one. Its a confined gas that is cycled through is processes and returned to its original state with maximum efficiency e carnot = e ideal = e max 33

34 Heat Engine formula summary Q H = W + Q C Q H = W + Q C t t t e = W Q H = Q H Q C Q H e = W/t Q H /t = Q H/t Q C /t Q H /t e max = T H T C T H 34

35 Ex: 10.) An engine manufacturer makes a claim that the heat input per second is 9 kj at 375 K. The heat output per second is 4 kj at 225 K. Do you believe these claims? 35

36 11.) A nuclear power plant operates at 75 % of its maximum efficiency between temperatures of 600 and 350 deg C. If the plant produces 1.3 GW, how much exhaust heat is discharged per hour. 36

Refrigerators Air conditioners basically the same Goal is to remove heat from a cold temperature location to make it

B) The compressor compresses gas which heats up as it is pressurized B C) The coils on the back of the refrigerator let

C) The high pressure liquid flows through the expansion valve (a small hole) to a low pressure area on the other side

37 Refrigerators Air conditioners basically the same Goal is to remove heat from a cold temperature location to make it colder. This is not a natural process so work has to be input to make it happen. B) The compressor compresses gas which heats up as it is pressurized B C) The coils on the back of the refrigerator let the hot gas dissipate its heat and gas condenses into liquid at high pressure. C) The high pressure liquid flows through the expansion valve (a small hole) to a low pressure area on the other side making the liquid boils and vaporizes into a gas of temperature 27 F. C A) The cold gas cycles through removing heat from the interior A) The cold gas is sucked up by the compressor, and the cycle repeat 37

38 Energy Flow Diagram refrigerator / air conditioner Heat Pump 38

39 Engine or Refrigerator? Can tell based on the PV diagram In an Engine In a Fridge 39

40 PRACTICE AP 1995B4. (10 points) A heat engine operating between temperatures of 500 K and 300 K is used to lift a 10 kilogram mass vertically at a constant speed of 4 meters per second. a. Determine the power that the engine must supply to lift the mass. b. Determine the maximum possible efficiency at which the engine can operate. c. If the engine were to operate at the maximum possible efficiency, determine the following. i. The rate at which the hot reservoir supplies heat to the engine ii. The rate at which heat is exhausted to the cold reservoir 40

41 1999B7 (10 points) A cylinder contains 2 moles of an ideal monatomic gas that is initially at state A with a volume of 1.0 x 2 10 m 3 and a pressure of 4.0 x 10 5 Pa. The gas is brought isobarically to state B. where the volume is 2.0 x 10 2 m 3. The gas is then brought at constant volume to state C, where its temperature is the same as at state A. The gas is then brought isothermally back to state A. a. Determine the pressure of the gas at state C. b. On the axes below, state B is represented by the point B. Sketch a graph of the complete cycle. Label points A and C to represent states A and C, respectively. (c) State whether the net work done by the gas during the complete cycle is positive, negative, or zero. Justify your answer (d) Determine the work done by the gas during process A B (e) Determine the heat added or removed during process A B (f) Determine the net heat added or removed during process A B C (g) State whether this device is a refrigerator or a heat engine. Justify your answer 41

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AP PHYSICS 2 WHS-CH-15 Thermodynamics Show all your work, equations used, and box in your answers!

AP PHYSICS 2 WHS-CH-15 Thermodynamics Show all your work, equations used, and box in your answers! Nicolas Léonard Sadi Carnot (1796-1832) Sadi Carnot was a French military engineer and physicist, often