Tells us the average translational kinetic energy of the particles

Transcription

1 Temperature and Heat What is temperature? Kinetic Energy What is heat? Thermal Expansion Specific Heat Latent Heat and phase changes Unit 03, Slide 1 Temperature Tells us the average translational kinetic energy of the particles Related to Internal Energy of system Unit 03, Slide 2 1

2 Temperature Scales Fahrenheit Water Freezes Water Boils Celcius Water Freezes Water Boils 32 o F 212 o F 0 o C 100 o C At standard pressure and temperature (STP) o F = 9/5 o C + 32 o o C = 5/9( o F 32 o ) Unit 03, Slide 3 Example 19.1: Temperature Conversion What is 40 o F in Celsius? o C = 5/9( o F 32 o ) = 5/9(40 o -32 o ) = 4.4 o C Double it, add 30 o Subtract 30 o, divide by 2 Unit 03, Slide 4 2

3 Temperature Scales II Does a gas have zero kinetic energy at zero degrees Celsius? Pressure o C 0 o C Temperature ( o C) o C = 0K( zero kelvin ) o F= 0 o R ( zero degrees Rankine ) Unit 03, Slide 5 Temperature and Velocity Recall: T <KE TRAN > ½ kt =<½mv x2 > Boltzman s Constant = 1.38X10-23 J/K v rms =[3kT/m] 0.5 KE AVG =3/2kT Unit 05 Kinetic Theory, Slide 6 3

4 Bridge Question 2a Two monoatomic gases, helium and neon, are mixed and in thermal equilibrium Bridge at temperature Question T. Therefore, 2a A. The helium atoms have the same average translational kinetic energy as the neon atoms. B. Each atom has a different average translational kinetic energy. C. There is a difference of 3/2 kt in the average translational kinetic energy between helium atoms and neon atoms. Kinetic Energy and Temperature Many of the molecules have different kinetic energies, but on average, the kinetic energy of a gas can be calculated using: K avg = 3 2 kt Boltzmann Constant 4

5 Bridge Question 2b If the molar mass of helium is 4.0 g/mol and the molar mass of neon is 20.2 g/mol, then A. All the atoms have exactly the same velocity. B. All the atoms have the same average speed. C. The average speed of the helium atoms is greater than the average speed of the neon atoms. D. The average speed of the neon atoms is greater than the average speed of the helium atoms. E. The atoms diffuse from high temperature to low temperature. Example 19.2: Gas Velocity What is the average velocity of a nitrogen (N 2 ) molecule in earth s atmosphere? (T=287K) What is the average velocity of a hydrogen (H 2 ) molecule in earth s atmosphere? (T=287K) Unit 05 Kinetic Theory, Slide 10 5

6 Variation with Temperature v rms = v peak 4 m f ( v) = ( ) 2kT mv 2kT v e Unit 05 Kinetic Theory, Slide 11 Variation with Mass Unit 05 Kinetic Theory, Slide 12 6

7 Hydrogen is the most common element in the universe. In fact, it s around 6000 more abundant than nitrogen. So why is there is little of it in the earth s atmosphere? a) It has decayed away via radioactivity. b) It has escaped the earth s gravity with its high velocity. c) It has been burned away in interactions with volcanic fire d) Hydrogen in not naturally formed in earth s crust while nitrogen is. Unit 05 Kinetic Theory, Slide 13 Thermal Expansion DL = a L o DT Material a (/C x10-6 ) Glass, ordinary 9 Glass, pyrex 4 Quartz, fused 0.59 Aluminum 24 Brass 19 Copper 17 Iron 12 Steel Platinum 9 Tungsten 4.3 Gold 14 Silver 18 Concrete Heat Transmission 4, Slide 14 7

8 Example 19.3: Thermal Expansion A 2.5 meter long rod of #6 reinforcing steel is placed inside a plate of concrete on the Stevenson Expressway. This rebar has a coefficient of thermal expansion of 10.1 X 10-6 / o C. If the Chicago weather changes from -10 o C to 35 o C, how much will the rod expand? Fluids Lecture 01, Slide 15 Thermal Expansion DL = a L o DT Material a (/C x10-6 ) Glass, ordinary 9 Glass, pyrex 4 Quartz, fused 0.59 Aluminum 24 Brass 19 Copper 17 Iron 12 Steel Platinum 9 Tungsten 4.3 Gold 14 Silver 18 Concrete Heat Transmission 4, Slide 16 8

9 Rebar Fluids Lecture 01, Slide 17 An aluminum rod has cross-sectional area of 10cm 3 and a length Expansion of 1m. When its temperature is changed from 20 o C to 30 o C, its length changes about 0.2mm. Which of the following would cause the length change to double to about 0.4mm. A. Doubling the final temperature to 60 o C B. Doubling the length of the rod to 2m. C. Changing the final temperature to 40 o C D. (A) and (B) E. (B) and (C) Heat Transmission 4, Slide 18 9

10 Thermal Expansion Loops Heat Transmission 4, Slide 19 Example 19.4: Thermal Volume Expansion A cube of brass is initially 3cm on a side. If the cube s temperature is raised from 20 o C to 95 o C, what is its final volume? Heat Transmission 4, Slide 20 10

11 Thermal Expansion of H 2 O dv dt = Expansion We saw that when I heated the alone sphere, it did not pass through the ring. What if I heat both the ring and the sphere? A. The sphere will pass through B. The sphere will not pass through Heat Transmission 4, Slide 22 11

12 Heat-Work-Temperature Work (W) - how mechanical energy is transferred into or out of a system Heat (Q) - how thermodynamic energy is transferred into or out of a system Work Heat Object can not contain heat. (Something can t contain work ) Unit 03, Slide 23 Heat Gravity can add transfer energy to ball via work (Dh 0) 280K 300K 280K transfer energy to box via heat (DT 0) Unit 03, Slide 24 12

13 Units Calorie = amount of energy to raise one gram of water from 14.5 o C to 15.5 o C British Thermal Unit (BTU) = amount of energy to raise one pound of water from 63 o F to 64 o F 1 Calorie = 3.97 X 10-3 BTU = Joule Unit 03, Slide 25 Temperature and Heat Heat (Q) Temperature(T) increases Q=C*DT Q=c*m*DT Q=c m *n*dt But how much? heat capacity specific heat capacity molar heat capacity Unit 03, Slide 26 13

14 Specific Heat c (kj/kg K) c m (kj/mole K) Unit 03, Slide 27 Example 19.5: Specific Heat Using a Bunsen burner in chemistry lab 25kJoule of heat is added to 0.32 kg of a liquid. The liquid s temperature goes from a room temperature of 20 o C to around 60 o C. What is the heat capacity of the amount of the liquid? What is the specific heat capacity of liquid? Unit 03, Slide 28 14

15 Two different objects, A and B, are raised to a temperature of C. They are then both placed in 1-liter water baths that are initially at a temperature of 20 0 C. After both systems have reached thermal equilibrium, one is at 25 0 C and one is at 30 0 C. What must be different about objects A and B? A. their heat capacity B. their specific heat capacity C. their mass D. (A) and (B) E. all of the above Specific Heat c (kj/kg K) c m (kj/mole K) Unit 03, Slide 30 15

16 Example 19.6: Specific Heat How much heat is needs to be added to raise 2kg of aluminum from 10 o to 20 o C? How much heat is needs to be added to raise 2kg of water from 10 o to 20 o C? Unit 03, Slide 31 When you eat hot pizza, it always seems like it s the cheese that burns your mouth and not the crust. What is that? a) because the cheese is hotter b) because the cheese is on the top of to pizza and the crust is on the bottom c) because the heat capacity of cheese is greater than the heat capacity of the crust Unit 03, Slide 32 16

17 Bridge Question 1 A potato and raisins salad has been warmed up to a temperature of 80 o C and let it stand for three minutes. Then one tries a bite. Would the potatoes and raisins be equally warm? Potatoes have a specific heat of 3430 J /kg o C. Raisins have a specific heat of 1630 J /kg o C. No. Potatoes will be warmer. No. Raisins will be warmer. Yes. Higher specific heat constant, harder to change temperature Example 19.7: Heat Transfer A 2.5kg block of aluminum at 20 o C is dropped into a bath of 2.5kg of water at 10 o C. The water and block are both placed inside a super insulator that will not allow any heat transfer in or out of the system. (Q NET =0) What is the final temperature of the block/water system after they come to thermal equilibrium? Unit 03, Slide 34 17

18 Physics 1201 A 2.5kg block of aluminum at 20oC is dropped into a bath of 2.5kg of water at 10oC. The specific heat of water is 4180 J/kg-K. The specific heat of aluminum is 900 J/kg-K. What can we say about the magnitude of the heat out of the aluminum (QA) and the magnitude of the heat into the water (QW)? A) QA < QW B) QA = QW Q=0 means adiabatic C) QA > QW Unit 03, Slide 35 A 2.5kg block of aluminum at 20oC is dropped into a bath of 2.5kg of water at 10oC. The specific heat of water is 4180 J/kg-K. The specific heat of aluminum is 900 J/kg-K. What can we say about the final temperature of the block/water system? A) It will be less than 15oC B) It will be 15oC C) It will be more than 15oC Unit 03, Slide 36 18

19 Latent Heat Q v = m*l v Temperat ure (T) Q v dt 1 = dq c Heat In (Q) L V = Latent Heat of Vaporization = amount of heat required to change the phase of 1kg from liquid to gas Unit 03, Slide 37 Latent Heats Unit 03, Slide 38 19

20 Bridge Question 3 The temperature of a 100-g piece of ice is risen steadily so that the ice converts first into liquid water and then evaporates completely, all at the same pressure of 1 atm. What of the following qualitative plots of temperature versus energy may represent best the process? Why steam is so dangerous Temperat ure (T) 101 o C 99 o C Heat In (Q) Unit 03, Slide 40 20

21 Boiling an Ice Cube An ice cube is about 2cm on a side so it contains about 8grams or of water. How much energy could it take to boil a single ice cube that started at -10 o C? Unit 03, Slide 41 Specific Heat c (kj/kg K) c m (kj/mole K) Unit 03, Slide 42 21

22 Latent Heats Unit 03, Slide 43 Example 19.18: Heat Transfer II A one liter bottle of Pepsi is placed in our super cooler along with six cubes of ice. The ice cubes are around 3cm on a side and so have a mass of 27gram each. The Pepsi starts out at room temperature (20 o C) and the ice starts at -10 o C. What is the final temperature after the system has come to thermal equilibrium? Unit 03, Slide 44 22