Chapter 13 The Transfer of Heat 13 1 Convection CONVECTION Convection is the process in which heat is carried from one place to another by the bulk movement of a fluid convection currents 13 1 Convection Conceptual Example 1 Hot Water Baseboard Heating and Refrigerators Hot water baseboard heating units are mounted on the wall next to the floor The cooling coil in a refrigerator is mounted near the top of the refrigerator Each location is designed to maximize the production of convection currents Explain how 13 1 Convection Thermals can be used by glider pilots to gain considerable altitude 13 1 Convection Forced Convection 13 2 Conduction CONDUCTION Conduction is the process whereby heat is transferred directly through a material with any bulk motion of the material playing no role in the transfer One mechanism for conduction occurs when the atoms or molecules in a hotter part of the material vibrate or move with greater energy than those in a cooler part By means of collisions the more energetic molecules pass on some of their energy to their less energetic neighbors Materials that conduct heat well are called thermal conductors and those that conduct heat poorly are called thermal insulators 13 2 Conduction The amount of heat Q that is conducted through the bar depends on a number of factors 1 2 3 4 The time during which conduction takes place The temperature difference between the ends of the bar The cross sectional area of the bar The length of the bar 13 2 Conduction CONDUCTION OF HEAT THROUGH A MATERIAL The heat Q conducted during a time t through a bar of length L and cross sectional area A is kA T t Q L SI Units of Thermal Conductivity J s m Co thermal conductivity 13 2 Conduction 13 2 Conduction Materials with dead air spaces are usually excellent thermal insulators 13 2 Conduction Example 4 Layered insulation One wall of a house consists of plywood backed by insulation The thermal conductivities of the insulation and plywood are respectively 0 030 and 0 080 J s m Co and the area of the wall is 35m2 Find the amount of heat conducted through the wall in one hour 13 2 Conduction Q Qinsulation Qplywood But first we must solve for the interface temperature kA T t kA T t L insulation L plywood 0 030 J s m C A 25 0 C T t 0 080 J s m C A T 4 0 C t 0 076 m T 5 8 C 0 019 m 13 2 Conduction 0 030 J s m C 35 m 25 0 C 5 8 C 3600 s Qinsulation 9 5 105 J 2 0 076 m 13 2 Conduction Conceptual Example 5 An Iced Up Refrigerator In a refrigerator heat is removed by a cold refrigerant fluid that circulates within a tubular space embedded within a metal plate Decide whether the plate should be made from aluminum or stainless steel and whether the arrangement works better or worse when it becomes coated with a layer of ice 13 3 Radiation RADIATION Radiation is the process in which energy is transferred by means of electromagnetic waves A material that is a good absorber is also a good emitter A material that absorbs completely is called a perfect blackbody 13 3 Radiation The emissivity e is a dimensionless number between zero and one It is the ratio of what an object radiates to what the object would radiate if it were a perfect emitter THE STEFAN BOLTZMANN LAW OF RADIATION The radiant energy Q emitted in a time t by an object that has a Kelvin temperature T a surface area A and an emissivity e is given by Q e T 4 At Stefan Boltzmann constant 5 67 10 8 J s m 2 K 4 13 3 Radiation Example 6 A Supergiant Star The supergiant star Betelgeuse has a surface temperature of about 2900 K and emits a power of approximately 4x1030W Assuming that Betelgeuse is a perfect emitter and spherical find its radius 4 Q e T At 4 r 2 13 3 Radiation 4 2 Q e T 4 r t Q t 4 1030 W r 4 4 8 2 4 4 e T 4 1 5 67 10 J s m K 2900 K 3 1011 m 13 4 Applications A thermos bottle minimizes heat transfer via conduction convection and radiation 13 4 Applications The halogen cooktop stove creates electromagnetic energy that passes through the ceramic top and is absorbed directly by the bottom of the pot