1. Physics Montwood High School R. Casao
Heat Exchange
Physics
Montwood High School
R. Casao

2. Temperature and Heat
When a soda can is taken out of the refrigerator and left on the kitchen table, its temperature will rise – rapidly at first but then more slowly – until the temperature of the soda equals that of the air in the room. At this point, the soda and the air temperature in the room are in thermal equilibrium.
The temperature of a hot cup of coffee left sitting on the table will fall until it also reaches thermal equilibrium with the air temperature in the room.
The change in temperature is due to the transfer of energy between object and the environment.

3. Temperature and Heat
Thermal energy: the total potential and kinetic energy associated with the random motion and arrangement of the particles of a material.
Heat, Q, is thermal energy that is absorbed, given up, or transferred from one body to another.
Heat is thermal energy in motion.
Heat is used when the transfer of thermal energy from one body to another body at a different temperature is involved.

5. Temperature and the Zeroth Law of Thermodynamics

6. Temperature and Heat
(a) Q is negative when heat energy is transferred to the environment from the system.
(b) Q = 0 J when the transfer of heat energy between the system and the environment is equal.
(c) Q is positive when heat energy is transferred to a system from the environment.

7. Specific Heat Capacity c
The specific heat capacity c of a solid or liquid is defined as the heat required to raise a unit mass of the substance by one degree of temperature.
Equation:
Unit: or

8. Heat Change
To determine the amount of thermal energy gained or lost by a mass:
Heat energy is gained if Q is positive.
Heat energy is lost if Q is negative.

9. Law of Heat Exchange
For a closed system in which heat energy cannot enter or leave, the heat lost by objects at a higher temperature is equal to the heat gained by objects at lower temperature until thermal equilibrium is reached (at which point the final temperature of both objects is the same).
The final temperature will be somewhere between the initial low temperature and the initial high temperature.

10. Law of Heat Exchange Conservation of Energy: Q lost = Q gained
To avoid problems with signs, for Q lost = Q gained problems, it is best to make T = Thi – Tlo

11. A Word About ΔT
In the thermal expansion/contraction problems, all materials were heated and cooled together from the same initial temperature to the same final temperature, so you could use ΔT = Tf – Ti.
In problems in which one object is heated to a final temperature and another object is cooled to the same final temperature, use ΔT = Thi – Tlo.

12. Heat Transfer by Conduction
Conduction is the transfer of thermal energy without any net movement of the material itself.
When a metal poker is put in a hot fire, the exposed end of the poker soon becomes hot as well, even though it is not directly in contact with the source of heat. We say that heat has been conducted from the hot end to the cold end.

13. Heat Transfer by Conduction
Heat conduction in many materials can be visualized as the result of molecular collisions. As one end of the object is heated, the molecules there move faster and faster. As they collide with their slower-moving neighbors, they transfer some of their energy to these molecules whose speeds thus increase. These in turn transfer some of their energy by collision with molecules farther along the object. Thus the energy of thermal motion is transferred by molecular collision along the object.

14. Heat Transfer by Conduction
In metals, it is the collisions of free electrons within the metal with each other and with metal atoms that is responsible for conduction. Most metals are good conductors of electricity because some electrons can leave their parent atoms and wander through the crystal lattice. These “free” electrons can carry energy from the hotter to the cooler regions of the metal. Good thermal conductors such as silver, copper, aluminum, and gold are also good electrical conductors.

15. Metals are different
The outer electrons for metal atoms drift, and are free to move.
When the metal is heated, this ‘sea of electrons’ gain kinetic energy and transfer it throughout the metal.
Insulators, such as wood and plastic, do not have this ‘sea of electrons’ which is why they do not conduct heat as well as metals.

16. Why does metal feel colder than wood, if they are both at the same temperature?
Metal is a conductor, wood is an insulator. The metal conducts the heat away from your hands, the wood does not conduct the heat away from your hands as well as the metal, so the wood feels warmer than the metal.

17. Heat Transfer by Conduction
Heat conduction takes place only if there is a difference in temperature, and the direction of heat flow is from higher to lower temperature. Indeed, it is found experimentally that the rate of heat flow through a substance is proportional to the difference in temperature between its ends. The rate of heat flow also depends on the size and shape of the object.

18. Heat Transfer by Conduction
The insulating properties of clothing come from the insulating properties of air. Without clothes, our bodies would heat the air in contact with the skin and would soon become reasonably comfortable because air is a very good insulator. But since air moves - there are breezes and drafts, and people themselves move about - the warm air would be replaced by cold air, thus increasing the temperature difference and the heat loss from the body. Clothes keep us warm by holding air so it cannot move readily. It is not the cloth that insulates us, but the air that the cloth traps. Down is a very good insulator because even a small amount of it fluffs up and traps a great amount of air.

19. Heat transfer occurs only between regions that are at different temperatures and the direction of heat flow is always from higher to lower temperature.
Heat conduction is usually described using the time rate of heat flow (Q/t) in a material for a given temperature difference (T).
Experiments have established that the rate of heat flow through a substance depends on the temperature difference between the boundaries.

20. Heat conduction also depends on the size of the object as well as its composition.
The top figure shows a rod of conducting material with cross-sectional area A and length L.
The left end of the rod is kept at temperature TH and the right end of the rod is kept at a lower temperature TC so heat flows from left to right.
The sides of the rod are insulated to prevent heat transfer at the sides.

21. When a quantity of heat dQ is transferred thru the rod in a time dt, the rate of heat flow is dQ/dt.
Heat current H = dQ/dt.
Equation:
k is a proportionality constant called the thermal conductivity of the material.
The quantity is the temperature difference
per unit length and is called the magnitude of the temperature gradient.
The numerical value of k depends on the material.

22. The greater the value of k for a material, the better it will conduct heat.
Units of k:
The heat current equation can be applied to any homogeneous body with uniform cross-section A perpendicular to the direction of flow; L or d is the length of the heat-flow path.
Units of H: Watt or J/s

23. In some problems, heat flows thru two different materials in succession.
The temperature at the interface between the two materials is between TH and TC and can be represented by T.
The temperature differences for the two materials are TH – T and T – TC.
In steady-state heat flow, the same heat has to pass thru both materials in succession, so the heat current H is the same for both materials.
If there are two parallel heat flow paths, so that some heat flows thru each path, then the total H is the sum of the quantities H1 and H2 for the separate paths. The temperature difference is the same for both paths, but L, A, and k may be different.

24. Heat Transfer by Convection
Convection is the process of heat transfer through the mass motion or flow of some fluid, such as air or water.
When a pot of water is heated, convection currents are set up as the heated water at the bottom of the pot rises because of its reduced density and is replaced by cooler water from above.

25. Heat Transfer by Convection
Although liquids and gases are generally not very good conductors of heat, they can transfer heat quite rapidly by convection. Convection is the process whereby heat is transferred by the mass movement of molecules from one place to another. Whereas conduction involves molecules (and/or electrons) moving only over small distances and colliding, convection involves the movement of molecules over large distances.

26. The particles spread out and become less dense.
What happens to the particles in a liquid or a gas when you heat them?
The particles spread out and become less dense.
A fluid is a liquid or a gas
This effects fluid movement.

27. Fluid Movement
Cooler, more dense fluids sink through warmer, less dense fluids.
In effect warmer liquids and gases rise up.
Cooler liquids and gases sink.

28. Styrofoam is an excellent thermal insulator because it contains many small, dead-air spaces. These small spaces inhibit heat transfer by convection currents, and air itself has a very low thermal conductivity.

29. Why is it windy at the seaside?

30. Heat Transfer by Radiation
Radiation is a more rapid transfer of thermal energy in the form of electromagnetic radiation accomplished by a process that requires neither contact nor mass flow.
A hot object also loses heat energy by radiation. This radiation is similar to light and can pass through empty space. The warmth you fell when you warm yourself by a fire is due to this radiation. If the object is hot enough, some of the radiation is visible and can indeed be seen.

31. The rate at which an object radiates energy is proportional to the fourth power of the object’s absolute temperature and is called Stefan’s law:
H = heat current radiated in Watts (J/s)
A = object’s surface area
T = object’s Kelvin temperature
 = Stefan-Boltzmann constant;  = 5.67 x 10-8 W/(m2·K4)
e = emissivity; a unitless number between 0 and 1 that is characteristic of the material
Dark surfaces have emissivity close to 1; shiny surfaces have emissivity close to 0.
Emissivity of human skin = 0.70

32. Dark surfaces not only are better emitters of radiation, they are also good absorbers of radiation.
To maintain a constant temperature, the incident energy absorbed must equal the emitted energy.
A good absorber is also a good emitter.
Ideal or perfect absorber and emitter is called a black body (e = 1).
Shiny surfaces are poor absorbers since most of the incident radiation is reflected.
Objects in thermal equilibrium with the surroundings have a constant temperature and are absorbing and emitting radiation at the same rate.
If the temperature of the object and its surroundings are different, there will be a net flow of radiant energy.

33. If an object is at temperature T and its surroundings are at temperature Ts, the net rate of energy loss or gain per unit time (power) is:
If Ts < T, then H will be negative, indicating a net heat energy loss.
Temperature must be in Kelvins.
It is possible to have energy transfer between an object and its surroundings, or between objects, at the same temperature.
There is a continuous exchange of radiant energy, but there is no net change of the internal energy of the object.

34. Since the color black is associated with nearly complete absorption of visible light, the term perfect blackbody or, simply, blackbody is used when referring to an object that absorbs all the electromagnetic waves falling on it.

35. A thermos bottle minimizes energy transfer due to convection, conduction, and radiation.

36. Q lost forging = Q gained oil
Heat Exchange Example
At a fabrication plant, a hot metal forging has a mass of 75 kg and a specific heat of 430 J/(kg·°C). To harden it, the forging is quenched by immersion in 710 kg of oil that has a temperature of 32° C and a specific heat of 2700 J/(kg·°C). The final temperature of the oil and forging at thermal equilibrium is 47° C. Assuming the heat flows only between the forging and the oil, determine the initial temperature of the forging.
Q lost forging = Q gained oil

37. Heat Exchange Example

38. Final Temperature Example
In an experiment, 0.5 kg of copper shot at 100° C is added to 5 kg of water at 10° C. What is the temperature of the mixture at thermal equilibrium?
Q lost copper = Q gained water
(m·c·DT)copper = (m·c·DT)water

39. Final Temperature Example

40. Conduction Example
Two slabs of thickness L1 and L2 and thermal conductivities k1 and k2 are in thermal contact with each other. The temperature of their outer surfaces are Tc and Th, with Th > Tc.
The temperature at the interface T and the rate of energy transfer (power P) by conduction through the slabs in the steady-state condition can be determined.

41. Steady-state condition means that energy transfers thru the compound slab at the same rate at all points.
If not, energy would be building up or disappearing at some point.
The temperature will vary in the two slabs, most likely at different rates in each part of the compound slab.
There will be a fixed temperature T at the interface when the system is in the steady state.
The rate of energy transfer (power) is the same in both slabs of material.
Heat energy flows from Th to Tc through the two slabs.

42. Conduction Example Rate of energy transfer thru slab 2:
When the steady-state is reached, P1 = P2:

43. Radiation Example
A student is trying to decide what to wear. The surroundings in his bedroom are at 20º C. If the skin temperature of the unclothed student is 35º C, what is the net energy loss from his body in 10 minutes by radiation? Assume that the emissivity of skin is 0.9 and that the surface area of the student is 1.5 m2.

44. The total energy lost by the skin in 10 minutes is: