Physics 111 Lecture 36 (Walker: 16.4-6) Heat Capacity & Specific Heat Heat Transfer May 1, 2009 Quiz (Chaps. 14 & 16) on Wed. May 6 Lecture 36 1/26 Heat Capacity (C) The heat capacity C of an object is the amount of heat that has to be added to it to raise its temperature by one degree. If we add heat Q and get temperature change T, then: Q is positive if T is positive; that is, if heat is added to a system. Q is negative if T is negative; that is, if heat is removed from a system. Lecture 36 2/26
Specific Heat (c) The specific heat c of a material is the heat capacity C of an object made from the material divided by the mass of the object. C c = m Since C = Q/ T, we could write this as: Lecture 36 3/26 Some specific heat values. Specific heats of gases are complicated and are measured at either constant pressure (c P ) or constant volume (c V ). Lecture 36 4/26
Example How much heat energy is needed to raise the temperature of 2 kg of copper (c = 387 J/kg-K) from 10 to 30 C? Q = mc T = (2 kg)(387 J/kg-K)(20K) = 1.55 x 10 4 J Lecture 36 5/26 Calorimetry A calorimeter is a lightweight, insulated cup or flask containing water. When an object is put in, the object and the water come to thermal equilibrium. If the mass of the flask can be ignored, and if the insulation keeps any heat from escaping or entering: 1. The final temperatures of the object and the water will be equal. 2. The total energy of the system is conserved. This allows us to calculate the specific heat of the object. Lecture 36 6/26
Calorimetry Solving Problems For the isolated system consisting of the object and the water, Energy out of one part = energy into another part Or: Q lost = Q gained Example: A piece of aluminum of mass 0.5 kg is heated to 100 C and placed in 0.4 kg of water initially at T=20 C in styrofoam cup. If final temperature of system is 37 C, what is c for aluminum? Q lost = Q gained m Al c Al (100 C-37 C) = m W c W (37 C-20 C) (0.5 kg)c Al (63 C) = (0.4kg)(4186J/kg-K)(17 C) c Al = 904 J/kg-K Lecture 36 8/26
Heat Transfer - Methods Conduction - Thermal kinetic energy passed from particle-to-particle along a length of material. Convection - Thermal energy carried by moving fluid. Radiation - Thermal energy carried by electromagnetic waves. Lecture 36 9/26 Heat Transfer: Conduction Heat conduction can be visualized as occurring through molecular collisions. Thermal kinetic energy is passed along as hotter particles collide with colder ones. Crosssectional area Q L
Conduction Experimentally, it is found that the amount of heat Q that flows through a rod: Increases proportionally to the crosssectional area A Increases proportionally to the temperature difference T from one end to the other Increases steadily with time t Decreases with the length L of the rod Depends on the material of the rod Lecture 36 11/26 Conduction Combining, we find: The constant k is called the thermal conductivity of the rod. It depends on the material from which the rod is made. Lecture 36 12/26
Thermal Conductivity Some typical thermal conductivities: Substances with high thermal conductivities are good conductors of heat; those with low thermal conductivities are good insulators. Vacuum has a thermal conductivity = 0. Lecture 36 13/26 Example Cooking pot has iron bottom 2 cm thick by 0.1 m 2 area and contains boiling water at 100 C. You need 2 MJ of heat energy to cook food. How long will it take if the flame temperature is 300 C and heat losses can be neglected? t = QL/(kA T) = (2x10 6 J)(0.02m)/[(80W/Km)(0.1m 2 )(200 C)] = 25s What if pot glass (k=0.84w/km)? t = 2500s Lecture 36 14/26
Heat Transfer: Conduction The insulation value of building materials is given in terms of thermal resistance R values rather than thermal conductivity: Here, l is the thickness of the material. Convection Convection is the flow of fluid due to a difference in temperatures, such as warm air rising. The fluid carries the heat with it as it moves. Natural convection: Warm fluid will rise because it is less dense then cold fluid. Lecture 36 16/26
Heat Transfer: Convection Convection occurs when heat flows by the mass movement of molecules from one place to another. It may be natural or forced (fans); both these examples are natural convection. Heat Transfer: Convection Many home heating systems are forced hot-air systems; these have a fan that blows the air out of registers, rather than relying completely on natural convection. Our body temperature is regulated by the blood; it runs close to the surface of the skin and transfers heat. Once it reaches the surface of the skin, the heat is released through convection, evaporation, and radiation, along with a slight bit of conduction. (In water, there is much more conduction.)
Radiation All objects give off energy in the form of radiation, as electromagnetic waves infrared, visible light, ultraviolet which, unlike conduction and convection, can transport heat through a vacuum. Objects that are hot enough will glow visibly first red, then yellow, white, and blue as temperature increases. Objects at body temperature radiate in the infrared, and can be seen with night vision binoculars. Lecture 36 19/26 Lecture 36 20/26
Radiation The amount of energy radiated per second by an object due to its temperature is proportional to its surface area and also to the fourth (!) power of its temperature. Radiated power also depends on emissivity e of the surface, which is a number between 0 and 1 that indicates how effective a radiator the object is. A perfect radiator ( black body ) would have e=1. A perfect reflector ( shiny object) would not radiate at all; e=0. Lecture 36 21/26 Radiation This behavior is contained in the Stefan- Boltzmann law: Here, e is the emissivity, and σ is the Stefan- Boltzmann constant: The temperature must be in Kelvin units! Lecture 36 22/26
Radiation If you are sitting in a place that is too cold, your body radiates and loses to convection more heat than it is producing. You will start shivering and your metabolic rate will increase unless you put on clothing that has good insulation and/or low emissivity ( space blanket.) Emissivity also determines how well a surface absorbs radiant energy. e = 1 perfect absorber (perfect black body) e = 0 perfect reflector (mirror) An object at temperature T in surroundings of temperature T s will both radiate and absorb power. The net radiated power is P net = eσa(t 4 -T s4 ) Example Person wants to burn off 400 Calories (1.7 x 10 6 J) by standing naked in ice cave at -10 C. How long will it take if cooling is by radiation only? Take e=0.9; A=1.5m 2 ; T = 37 C = 310K; Ts = -10 C = 263K Pnet = eσa(t 4 -T s4 ) =(0.9)(5.7x10-8 W/m 2 K 4 )(1.5m 2 )[(310K) 4 -(263K) 4 ] = 340W Q = Pt, so t=1.7x10 6 J/340W= 4900s = 1.4hr Lecture 36 24/26
Radiation If you are in the sunlight, the Sun s radiation will warm you. The intensity of solar radiation is 1000 W/m 2. In general, you will not be perfectly perpendicular to the Sun s rays, and will absorb energy at the rate: Seasons This cos θ effect is also responsible for the seasons.
Heat Transfer: 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. End of Lecture 36 For Monday, May 4, read Walker 17.1-2. Homework Assignment 16b is due at 11:00 PM on Monday, May 4. Quiz (Chaps. 14 & 16) on Wed. May 6 Lecture 36 28/26