1. Ying Yi PhD Chapter 11 Energy in Thermal Processes 1 PHYS I @ HCCS

2. Outline PHYS I @ HCCS 2 Heat and internal Energy Specific Heat Latent heat and Phase Change Energy Transfer

3. When two objects of different temperatures are placed in thermal contact, the temperature of the warmer decreases and the temperature of the cooler increases The energy exchange ceases when the objects reach thermal equilibrium The concept of energy was broadened from just mechanical to include internal PHYS I @ HCCS 3

4. Internal Energy Internal Energy, U, is the energy associated with the microscopic components of the system Includes kinetic and potential energy associated with the random translational, rotational and vibrational motion of the atoms or molecules Also includes any potential energy bonding the particles together PHYS I @ HCCS 4

5. Heat Heat is the transfer of energy between a system and its environment because of a temperature difference between them The symbol Q is used to represent the amount of energy transferred by heat between a system and its environment PHYS I @ HCCS 5

6. Units of Heat Calorie An historical unit, before the connection between thermodynamics and mechanics was recognized A calorie is the amount of energy necessary to raise the temperature of 1 g of water from 14.5° C to 15.5° C. 1 cal = 4.186 J PHYS I @ HCCS 6

7. Example 11.1 Working out breakfast PHYS I @ HCCS 7 A student eats a breakfast consisting of a bowl of cereal and milk, containing a total of 3.20×10 2 Calories of energy. He wishes to do an equivalent amount of work in the gymnasium by performing curls with a 25.0-kg barbell. How many times must he raise the weight to expend that much energy? Assume he raises it through a vertical displacement of 0.400 m each time, the distance from his lap to his upper chest.

8. James Prescott Joule 1818 – 1889 British physicist Conservation of Energy Relationship between heat and other forms of energy transfer PHYS I @ HCCS 8

9. Specific Heat Every substance requires a unique amount of energy per unit mass to change the temperature of that substance by 1° C The specific heat, c, of a substance is a measure of this amount SI units: J / kg °C Historical units: cal / g °C PHYS I @ HCCS 9

10. Specific Heats Table PHYS I @ HCCS 10

11. Heat and Specific Heat Q = m c Δ T Δ T is always the final temperature minus the initial temperature When the temperature increases, Δ T and Δ Q are considered to be positive and energy flows into the system When the temperature decreases, Δ T and Δ Q are considered to be negative and energy flows out of the system PHYS I @ HCCS 11

12. A Consequence of Different Specific Heats Water has a high specific heat compared to land On a hot day, the air above the land warms faster The warmer air flows upward and cooler air moves toward the beach PHYS I @ HCCS 12

13. Example 11.2 Stressing a strut A steel strut near a ship’s furnace is 2.00 m long, with a mass of 1.57 kg and cross-sectional area of 1.00×10 -4 m 2. During operation of the furnace, the strut absorbs a net thermal energy of 2.50×10 5 J. (a) Find the change in temperature of the strut. (b) Find the increase in length of the strut. (c) If the strut is not allowed to expand because it’s bolted at each end, find the compressional stress developed in the strut. PHYS I @ HCCS 13

14. Energy transfer in a system In some cases it may be difficult to determine which materials gain heat and which materials lose heat You can start with  Q = 0 Each Q = m c  T Use T f – T i You don’t have to determine before using the equation which materials will gain or lose heat PHYS I @ HCCS 14

15. Problem Solving Hint It is important to organize the information in a problem A table will be helpful Headings can be Q material m c T f T i PHYS I @ HCCS 15

16. Example11.4 Calculate an Equilibrium Temperature PHYS I @ HCCS 16 Suppose 0.400 kg of water initially at 40.0 °C is poured into a 0.300 kg glass beaker having a temperature of 25.0°C. A 0.500 kg block of aluminum at 37.0°C is placed in the water and the system insulated. Calculate the final equilibrium temperature of the system.

17. Phase Change PHYS I @ HCCS 17 Note that: Phases changes involve a change in the internal energy, but no change in temperature

18. Latent Heat During a phase change, the amount of heat is given as Q = ±m L L is the latent heat of the substance Latent means hidden L depends on the substance and the nature of the phase change Choose a positive sign if you are adding energy to the system and a negative sign if energy is being removed from the system PHYS I @ HCCS 18

19. Latent Heat, cont. SI units of latent heat are J / kg Latent heat of fusion, L f, is used for melting or freezing Latent heat of vaporization, L v, is used for boiling or condensing Table 11.2 gives the latent heats for various substances PHYS I @ HCCS 19

20. Sublimation Some substances will go directly from solid to gaseous phase Without passing through the liquid phase This process is called sublimation There will be a latent heat of sublimation associated with this phase change PHYS I @ HCCS 20

21. Graph of Ice to Steam PHYS I @ HCCS 21

22. Warming Ice Start with one gram of ice at –30.0º C During A, the temperature of the ice changes from –30.0º C to 0º C Use Q = m c Δ T Will add 62.7 J of energy PHYS I @ HCCS 22

23. Melting Ice Once at 0º C, the phase change (melting) starts The temperature stays the same although energy is still being added Use Q = m L f Needs 333 J of energy PHYS I @ HCCS 23

24. Warming Water Between 0º C and 100º C, the material is liquid and no phase changes take place Energy added increases the temperature Use Q = m c Δ T 419 J of energy are added PHYS I @ HCCS 24

25. Boiling Water At 100º C, a phase change occurs (boiling) Temperature does not change Use Q = m Lv 2 260 J of energy are needed PHYS I @ HCCS 25

26. Heating Steam After all the water is converted to steam, the steam will heat up No phase change occurs The added energy goes to increasing the temperature Use Q = m c Δ T To raise the temperature of the steam to 120°, 40.2 J of energy are needed PHYS I @ HCCS 26

27. Problem Solving Strategies Make a table A column for each quantity A row for each phase and/or phase change Use a final column for the combination of quantities Use consistent units PHYS I @ HCCS 27

28. Problem Solving Strategies, cont Apply Conservation of Energy Transfers in energy are given as Q=mc Δ T for processes with no phase changes Use Q = m L f or Q = m L v if there is a phase change Start with  Q = 0 Or Q cold = - Q hot, but be careful of sign Δ T is T f – T i Solve for the unknown PHYS I @ HCCS 28

29. Example 11.5 Ice Water PHYS I @ HCCS 29 At a party, 6.00 kg of ice at -5.00 °C is added to a cooler holding 30 liters of water at 20.0°C. What is the temperature of the water when it comes to equilibrium?

30. Example 11.6 Partial Melting PHYS I @ HCCS 30 A 5.00 kg block of ice at 0°C is added to an insulated container partially filled with 10.0 kg of water at 15.0°C. (a) Find the final temperature, neglecting the heat capacity of the container. (b) Find the mass of the ice that was melted.

31. Methods of Heat Transfer Need to know the rate at which energy is transferred Need to know the mechanisms responsible for the transfer Methods include Conduction Convection Radiation PHYS I @ HCCS 31

32. Examples PHYS I @ HCCS 32 Conduction Convection Radiation

33. Resisting Energy Transfer Dewar flask/thermos bottle Designed to minimize energy transfer to surroundings Space between walls is evacuated to minimize conduction and convection Silvered surface minimizes radiation Neck size is reduced PHYS I @ HCCS 33

34. Thank you PHYS I @ HCCS 34