# Heat Transfer. Phys101 Lectures 35, 36. Key points: Heat as Energy Transfer Specific Heat Heat Transfer: Conduction, Convection, Radiation

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1 Phys101 Lectures 35, 36 Heat Transfer Key points: Heat as Energy Transfer Specific Heat Heat Transfer: Conduction, Convection, Radiation Ref: 16-1,3,4,10. Page 1

2 19-1 Heat as Energy Transfer We often speak of heat as though it were a material that flows from one object to another; it is not. Rather, it is a form of energy. Unit of heat: calorie (cal) 1 cal is the amount of heat necessary to raise the temperature of 1 g of water by 1 Celsius degree. Don t be fooled the calories on our food labels are really kilocalories (kcal or Calories), the heat necessary to raise 1 kg of water by 1 Celsius degree.

3 19-1 Heat as Energy Transfer If heat is a form of energy, it ought to be possible to equate it to other forms. The experiment below found the mechanical equivalent of heat by using the falling weight to heat the water: J = 1 cal kj = 1 kcal

4 19-1 Heat as Energy Transfer Definition of heat: Heat is energy transferred from one object to another because of a difference in temperature. Remember that the temperature of a gas is a measure of the kinetic energy of its molecules.

5 Example 19-1: Working off the extra calories. Suppose you throw caution to the wind and eat too much ice cream and cake on the order of 500 Calories. To compensate, you want to do an equivalent amount of work climbing stairs or a mountain. How much total height must you climb?

6 19-3 Specific Heat The amount of heat required to change the temperature of a material is proportional to the mass and to the temperature change: The specific heat, c, is characteristic of the material. Some values are listed at left.

7 Example 19-2: How heat transferred depends on specific heat. (a) How much heat input is needed to raise the temperature of an empty 20-kg vat made of iron from 10 C to 90 C? (b) What if the vat is filled with 20 kg of water?

8 19-4 Calorimetry Solving Problems Closed system: no mass enters or leaves, but energy may be exchanged Open system: mass may transfer as well Isolated system: closed system in which no energy in any form is transferred For an isolated system, energy out of one part = energy into another part

9 19-4 Calorimetry Solving Problems Example 19-3: The cup cools the tea. If 200 cm 3 of tea at 95 C is poured into a 150-g glass cup initially at 25 C, what will be the common final temperature T of the tea and cup when equilibrium is reached, assuming no heat flows to the surroundings?

10 19-4 Calorimetry Solving Problems The instrument to the left is a calorimeter, which makes quantitative measurements of heat exchange. A sample is heated to a well-measured high temperature and plunged into the water, and the equilibrium temperature is measured. This gives the specific heat of the sample.

11 Example 19-4: Unknown specific heat determined by calorimetry. An engineer wishes to determine the specific heat of a new metal alloy. A kg sample of the alloy is heated to 540 C. It is then quickly placed in kg of water at 10.0 C, which is contained in a kg aluminum calorimeter cup. (We do not need to know the mass of the insulating jacket since we assume the air space between it and the cup insulates it well, so that its temperature does not change significantly.) The final temperature of the system is 30.5 C. Calculate the specific heat of the alloy.

12 19-10 Heat Transfer: Conduction, Convection, Radiation Heat conduction can be visualized as occurring through molecular collisions. The heat flow per unit time is given by:

13 19-10 Heat Transfer: Conduction, Convection, Radiation The constant k is called the thermal conductivity. Materials with large k are called conductors; those with small k are called insulators.

14 Example 19-13: Heat loss through windows. A major source of heat loss from a house is through the windows. Calculate the rate of heat flow through a glass window 2.0 m x 1.5 m in area and 3.2 mm thick, if the temperatures at the inner and outer surfaces are 15.0 C and 14.0 C, respectively.

15 19-10 Heat Transfer: Conduction, Convection, Radiation Building materials are measured using R- values rather than thermal conductivity: Here, is the thickness of the material.

16 19-10 Heat Transfer: Conduction, Convection, Radiation Convection occurs when heat flows by the mass movement of molecules from one place to another. It may be natural or forced; both these examples are natural convection.

17 19-10 Heat Transfer: Conduction, Convection, Radiation Radiation is the form of energy transfer we receive from the Sun; if you stand close to a fire, most of the heat you feel is radiated as well. The energy radiated has been found to be proportional to the fourth power of the temperature:

18 19-10 Heat Transfer: Conduction, Convection, Radiation The constant σ is called the Stefan-Boltzmann constant: The emissivity ε is a number between 0 and 1 characterizing the surface; black objects have an emissivity near 1, while shiny ones have an emissivity near 0. It is the same for absorption; a good emitter is also a good absorber.

19 Example 19-14: Cooling by radiation. An athlete is sitting unclothed in a locker room whose dark walls are at a temperature of 15 C. Estimate his rate of heat loss by radiation, assuming a skin temperature of 34 C and ε = Take the surface area of the body not in contact with the chair to be 1.5 m 2.

20 19-10 Heat Transfer: Conduction, Convection, Radiation If you are in the sunlight, the Sun s radiation will warm you. In general, you will not be perfectly perpendicular to the Sun s rays, and will absorb energy at the rate:

21 19-10 Heat Transfer: Conduction, Convection, Radiation This cos θ effect is also responsible for the seasons.

22 19-10 Heat Transfer: Conduction, Convection, Radiation Thermography the detailed measurement of radiation from the body can be used in medical imaging. Warmer areas may be a sign of tumors or infection; cooler areas on the skin may be a sign of poor circulation.

23 Example 19-15: Star radius. The giant star Betelgeuse emits radiant energy at a rate 10 4 times greater than our Sun, whereas its surface temperature is only half (2900 K) that of our Sun. Estimate the radius of Betelgeuse, assuming ε = 1 for both. The Sun s radius is r S = 7 x 10 8 m.

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