Physics of Energy and the Environment

Transcription

1 Physics 161: Physics of Energy and the Environment October 23, 2008 Prof. Raghuveer Parthasarathy Fall 2008

2 Lecture 8: Announcements Reading: Wolfson, Chapter 4 Homework: Problem Set 4. Due Today, Oct. 23 Midterm: Thurs. Oct. 30 Covers material through Oct. 23 & PS4 Short answer + simple calculations No books, no calculators Additional advice, comments later. RP s office hours next week: Monday: pm Tuesday: Cancelled.

3 PS3 results Good! Median (of nonzero scores = 21 out of 25)

4 Last Lecture Heat flow by conduction: expected form k is thermal conductivity, a material property Heat flow by radiation: H ka Δ = T d hotter more radiation hotter shorter wavelengths spectrum of wavelengths Radiated power P = εσat 4 [strong T dependence] ε = emissivity. Max (=1) for black objects

5 Heat Capacity Suppose you supply energy (of any form), how much does T change? The relation between energy, Q, and ΔT depends on how much material there is: Mass, M intrinsic property: specific heat, c text s symbol, commonly used for heat.

6 Q = McΔT Heat Capacity (SI) units for c: J / kg / K e.g. water has c = 4184 J / kg / K. To raise the temperature of 1 kg of water (= 1 liter) by 10 C takes 41,840 Joules. Similarly, if 1 kg of water cools by 10 C, it transfers 41,840 J of heat. Note a difference of 10 C is the same as a difference of 10 K.

7 Q = McΔT Heat Capacity (SI) units for c: J / kg / K e.g. water has c = 4184 J / kg / K. To raise the temperature of 1 kg of water (= 1 liter) by 10 C takes 41,840 Joules. If we heated the 1kg of water above in 100 seconds, what power would we be expending?

8 Q = McΔT Heat Capacity An iron thumbtack and a big iron bolt are removed from a hot oven. They are red hot and have the same temperature. When dropped into identical containers of water of equal temperature, which one raises the water temperature more? A. thumbtack B. bolt

9 Q = McΔT Heat Capacity An iron thumbtack and a big iron bolt are removed from a hot oven.... which one raises the water temperature more? A. thumbtack B. bolt Same ΔT, same c. Bolt: higher M More heat (Q) transferred as it cools Larger ΔT for the water.

10 Heat Capacity of Water Water has a large heat capacity ( 4 5 typical substances) Important! It takes a lot of energy to change the temperature of water. Explains: hot water bottles (stay warm a long time) water cooled car radiators (& other machines) on and off shore breezes water takes longer to heat & longer to cool than land, & so they re often at different temperatures.

11 Heat Capacity of Water E. g. It takes more sunlight to warm the ocean than the land, so the two are often at different temperatures. ΔT Convection breezes. Bodies of water tend to moderate climates. Explains: mild climates in Northern Europe (& cold shores in Oregon and California) water stays warm as gulf stream currents carry it from the gulf of Mexico north & east to Europe

12 Heat Capacity of Water

13 Heat Capacity of Water Iceland is not ice covered like Greenland and parts of Siberia, even though it is nearly on the Arctic Circle. The average winter temperature of Iceland is considerably higher than regions at the same latitude in eastern Greenland and central Siberia. Why is this so?

14 ? Heat Input Temperature rises (usually) Can you think of a situation in which adding heat does not lead to a change in temperature?... istockphoto.com

15 Latent Heat Phase transitions (e.g. ice water, water steam) often involve a heat of transformation or latent heat to alter the intermolecular arrangements Latent heat = Energy required per unit mass (e.g. water melting: 334 kj/kg) E.g. ice at 10 C; add heat... T rises... 6 C... 3 C... 0 C continue to add heat. T remains at 0 C, but ice water... all ice has melted continue to add heat. T of water rises...

16 Physics of Energy Our survey of the Physics of Energy is complete Energy, Power Forms of Energy and Energy Conversion Thermal Energy and Heat

17 Coming Attractions Next: A bit of review (note: midterm Thurs.) + thoughts on how to think about physical relations Then: Specific Sources of Energy Climate and Climate Change

18 How to study Review: Lecture notes, especially questions Homework (see solutions) Understand: concepts how to do problems Understand means: Could you explain it to someone else?

19 Explanation E.g.: Explain how hydroelectric plants generate electricity. Discuss the various forms of energy involved there are more than two. Discuss the principles involved in final step of creating electrical energy.

20 Topics A non exhaustive list of important topics: Work, Power, Energy (meanings) Forms of energy Temperature and thermal energy Heat transfer Be able to: convert units do simple, rough calculations

21 Remember Numbers to remember: U. S. average power consumption per capita Typical human power scale That s it. No conversion factors. No energy statistics. Memorizing these is a waste of your mind. Equations to remember: relations between Work, Power, Energy SI units for these Kinetic & gravitational potential energy

22 How to study But what about all the other equations? It s important to understand... the meaning of various relations the physical bounds & behaviors of various relations... rather than memorizing equations For example...

23 Properties of the Carnot Efficiency What determines the Carnot efficiency? What does efficiency in general mean? What does the Carnot efficiency mean? What factors does it depend on? Is it bounded? [Ask]

24 Properties of the Carnot Efficiency What determines the Carnot efficiency? What does efficiency in general mean? efficiency = Mechanical work out / Heat energy in I m stressing that it s the energy flowing in due to a temperature difference

25 Properties of the Carnot Efficiency Even without knowing the correct e max expression, how would you conclude that these are incorrect : e e max max TC = T T = T 3 C H H [both wrong]

26 Dimensional Analysis This brings us to an interesting topic, or meta topic... Despite what you ve seen on TV, scientists, at least good ones, don t memorize lots of facts. Rather, they learn a lot from simple relations. Here s a powerful way of looking at the world...

27 Dimensions The same physical property can be described by different units, and we can convert between different units. It s fine (& correct) to say 2.54 cm = 1 inch. Different physical properties are different! A statement like 3 mph = 4 feet is nonsense, no matter the numbers used.

28 Dimensions Different physical properties have different dimensions. (A term not related to dimensions of space and time.) Three fundamental dimensions of length (L), mass (M), and time (T), from which all others can be constructed. For example: speed = length / time. All descriptions of speed must have this form! (miles per hour; meters per second; etc.)

29 Dimensions Often we write, e.g., [speed] = L/T The brackets [] mean dimensions of

30 Dimensional Analysis Why is it useful to think about dimensions? Because every correct physical relation must be dimensionally correct! This helps us check relations we derive. It also helps us construct new relations! A simple yet deep concept and one that s rarely taught.

31 Dimensional Analysis example Suppose we remember Gravitational potential energy E grav = M g h Suppose we don t remember the kinetic energy formula E kinetic = ½ Mv 2, but we recall that it s either: E kinetic = ½ Mv E kinetic = ½ Mv 2 E kinetic = ½ M 2 v Which is it?

32 Dimensional Analysis example Energy is energy all forms of energy have the same dimensions. What are the dimensions of gravitational potential energy? E grav = M g h, so [E grav ] = [M][g][h] [M] = M [h] = L, since height is a measure of length [g] =? Recall g is the acceleration due to gravity, g = 9.8 m/s 2. So [g] = L / T 2.

33 Dimensional Analysis example Therefore [E grav ] = [M][g][h] = M (L / T 2 ) L = M L 2 / T 2. Return to the kinetic energy possibilities E kinetic = ½ Mv E kinetic = ½ Mv 2 E kinetic = ½ M 2 v What is [v]? [v] = L / T

34 Dimensional Analysis example Therefore [E grav ] = [M][g][h] = M (L / T 2 ) L = M L 2 / T 2. Return to the kinetic energy possibilities E kinetic = ½ M v: dimensions M L / T E kinetic = ½ M v 2 : dimensions M (L / T) 2 = M L 2 / T 2. E kinetic = ½ M 2 v: dimensions M 2 L / T So: E kinetic = ½ Mv 2!

35 Kinetic Energy again Here s an even deeper view: Suppose we figure out (e.g. from experiments) that Kinetic Energy depends on mass and velocity. That s all we know. Can we figure out E kinetic = ½ Mv 2? We know [E] = M L 2 / T 2. We know [M] = M and [v] = L/T. We suppose E = # M a V b, where # is some number and a and b are also numbers. What do we see?

36 Kinetic Energy again We know [E] = M L 2 / T 2. We know [M] = M and [v] = L/T. We suppose E kinetic = # M a v b, where # is some number and a and b are also numbers. What do we see? For the M s to match, we need a=1. For the L s and T s to match, we need b=2. Therefore E kinetic = # Mv 2! # is some number we can t figure out that it s ½ just from dimensional analysis.

37 Dimensionless numbers # is some number we can t figure out that it s ½ just from dimensional analysis. (Often, the plain numbers 1, i.e. not ) Plain numbers are dimensionless. (We say their dimension is 1 see below.) Ratios formed by quantities that are dimensionally the same are dimensionless e.g. the Mach number = speed / speed of sound, so [Mach] = [v]/[v] = 1.

38 Dimensionless... Which of the following is dimensionless: A. The thermodynamic efficiency, e, of a heat engine B. Thermal conductivity C. The ratio of the gravitational potential energy of an object to its height D. Force

39 Dimensionless... A. The thermodynamic efficiency, e, of a heat engine B. Thermal conductivity C. The ratio of the gravitational potential energy of an object to its height D. Force What are the dimensions of efficiency? efficiency = Mechanical work out / Heat energy in [efficiency] = 1 (dimensionless)

40 Dimensionless efficiency efficiency = Mechanical work out / Heat energy in [efficiency] = 1 (dimensionless) Is our Carnot relation consistent with this? A. yes B. no e max = T 1 C Again, a way to discard obviously wrong relations T H

41 Dimensionless efficiency Is this wrong Carnot relation dimensionally correct? A. yes B. no e max T C = 1 TH 2

42 Dimensionless efficiency Is this wrong Carnot relation dimensionally correct? e max T C = 1 TH 2 A. yes B. no It s wrong, but dimensionally correct! (Don t get too cheerful about dimensional analysis!)

43 Dimensional Analysis Dimensionally wrong relations are necessarily wrong a good way to check! Constructingdimensionally correct equations can reveal physical relationships (except for dimensionless factors) Dimensionally correct relations are not necessarily correct.

44 Dimensional Analysis

45 Dimensional Analysis A famous example of dimensional analysis: Following the development of atomic weapons in the 1940 s, the energy released by an atomic bomb blast was maintained as classified, secret information. Life magazine published photos of the blasts, showing the expanding fireball at a series of times following detonation. From these publicly available photos, G. I. Taylor, a very clever physicist, figured out the value of E. by constructing a relation between the energy, the blast radius, time, and the density of air. There s only one such dimensionally correct relation possible! (Like our kinetic energy example.)