Energy in Thermal Processes Heat and Internal Energy Internal energy U: associated with the microscopic components of a system: kinetic and potential energies. The larger the number of internal degrees of freedom of a system (translation, rotation or vibrations of molecules) the larger the internal energy. Heat is the mechanism by which there is energy transferred Q between a system and the environment because of a temperature gradient. 1
Units of Heat One calorie is the energy required to raise the temperature of 1g of water from 14.5 0 C to 15.5 0 C Units 1 cal 4. 186 J Specific Heat The amount of energy per unit mass required to change the substance s temperature by 1 0 C. (It is an intrinsic property of each substance). c Q m T Units 1 J / kg 0 C 2
Specific heat: questions The specific heat of A is larger than that of B and both are at temperature T. Mass of A is the same as mass of B. Which system will require more energy transferred by heat to double its temperature? a) A b) B c) both require the same? You have 1 kg of iron, 1 kg of glass and 1kg of water, all at 10 0 C. Which of the three will be at highest temperature after 100 J of energy is transferred to each? Specific heat given in cal/g C. a) Iron (0.107) b)glass (0.2) c) water (1.0) Units of Heat: example A diet doctor encourages people to diet by drinking ice water. His theory is that the body must burn off enough fat to raise the temperature of the water from 0 0 C to 37.0 0 C. How many liters of ice water would have to be consumed to burn off 454g of fat? (Assume that this amount of fat requires 3500 Kcal to be transferred to the ice. 1 liter= 1000cm 3 and the density of water is 1.00 g/cm 3 ). 3
Calorimetry The principle of energy conservation requires that the energy that leaves the warmer substance equals the energy that enters the colder one. m c c c Q = cold Q hot How do we determine the specific heat of a substance? ( T Tc ) = mhch ( T Th ) c h mccc ( T Tc ) = m ( T T ) (Water is typically used for the cooling process) h h Specific heat: example Calculate the specific heat of a metal from the following data. A container made of a metal has mass 3.6 Kg and contains 14 Kg of water. A 1.8 Kg piece of the metal initially at a temperature of 180 0 C is dropped in the water. The container and the water are initially at 16 0 C. The final temperature of the whole system is 18 0 C. a) Neglect the change in temperature of the container. b) How does the result change when you account for the change in temperature of the container? 4
Latent heat and phase change Sometimes a transfer of energy does not result in a temperature increase: it may go into different forms of internal energy (phase change). Q = ±ml Latent heat of fusion L f is the energy required to melt (+) or freeze(-) one unit mass of the substance. Latent heat of vaporization L v is the energy required to boil (+) or condense (-) one unit mass of the substance. Latent heat and phase change 5
Latent heat: example Consider the addition of energy to 1g of ice at 30 0 C in a container held at constant pressure. Suppose that this energy results in the ice turning into steam at 120 0 C. The figure shows the experimental measurement of temperature as energy is added to the system. Explain the process and the energy quantities shown. (c ice =2090, c water =4186, c steam =2010, L f =3.33x10 5, L v =2.26x10 6 all in SI) Latent heat: example A 150 g copper bowl contains 220 g of water, both at 20.0 0 C. A very hot 300 g copper cylinder is dropped into the water causing the water to boil, with 5.00 g being converted to steam. The final temperature of the system is 100 0 C. Specific heats in SI units are 4186 for water and 387 for copper. Latent heat of vaporization for water is 2.26 MJ/kg. a) How much energy is transferred to the water? b) How much energy is transferred to the bowl? c) What was the original temperature of the cylinder? 6
Energy transfer Classification of Energy Transfer: Radiation Convection Conduction Thermal Conduction A difference in temperature drives the flow of energy from a hot part of the system to the cold part. the Rate of energy transfer is proportional to the cross-sectional area of the slab and the temperature difference, and inversely proportional to the thickness of the slab Q A( Th Tc ) P t = k L Thermal conductivity 7
Thermal conductivities (k) SI Units 1W / mk Thermal conduction: home insultation 8
Thermal conductivity One can derive an expression for the rate of energy transfer through a compound slab: Q P = = t A( Th T L / k In engineering the term L/k is usually referred to a R-value of the material (resistance to thermal conduction) Q P = = t A( T h i c i T R i c ) ) Resistance to thermal conduction (R) 9
Thermal conduction: questions Materials having high thermal conductivity provide better insulation than materials having low thermal conductivity. a) True b) false The thermal resistance of wall A is larger than that of wall B. Which of the following statements is correct: a) Wall A is best at insulating the house because it allows for larger energy transfer rate b) Wall A is best at insulating the house because it reduced the energy transfer rate c) Wall B is best at insulating the house because it allows for larger energy transfer rate d) Wall B is best at insulating the house because it reduces the energy transfer rate Thermal conduction: questions A board of length L and thermal conductivity k is used to insulate one wall. Another board of length 2L and thermal conductivity 2k, is used to insulate another wall of the area in the same house. In which wall is the rate of energy transfer larger? a) The first b)the latter c) both the same 10
Thermal conduction: example a) Calculate the rate at which body heat is conducted through the clothing of a skier in a steady-state process, given the following data: the body surface area is 1.8 m 2 and the clothing is 1.0 cm thick; the skin surface temperature is 33 0 C, whereas the outer surface of the clothing is at 1.0 0 C; the thermal conductivity of the clothing is 0.040 W/m K. b) How would the answer a) change if the skier s clothes became soaked with water of thermal conductivity 0.60 W/mK? Convection Energy transfer by the movement of the substance is referred to as convection. Natural convection results from a flow due to differences in densities Forced convection happens when a fan or a pump force the motion of hot air or hot water in heating systems 11
Thermal processes: questions A house has an electric heating system uniquely based on heating pads placed on a black ceiling. Why is this system not effective? a) Because one cannot reach the ceiling b) Because natural convection does not move the air around c) Because a black ceiling does not radiate Radiation All objects radiate energy continously in form of electromagnetic waves (ex: light). The rate at which an object radiates energy is known as Stephan s Law P = σaet 4 P = power in Watts s= constant (5.669x10-8 W/m 2 K 4 ) A= surface area e=emissivity (varies from 0 to 1) T= temperature (in Kelvin!) e=1 ideal absorber (black body) e=0 ideal reflector 12
Radiation Any object at a temperature T(obj) radiates energy but also absorbs energy from its surroundings at a temperature T(ext). The net effect will be P net = σae( T 4 obj T 4 ext ) When an object is in thermal equilibrium the rate at which is radiates equals the rate at which it absorbs energy. So the net rate is zero and it s temperature remains constant. Radiation: questions Stars A and B have the same temperature and emissivity, but star A has twice the radius of star B. What is the ratio of star A s power output to star B s power output due to radiation? a) 2 b) 4 c) 8 d) 16 Stars A and B have the same radius and emissivity. Star A has twice the absolute temperature of star B. What is the ratio of star A s power output to star B s power output due to radiation? a) 2 b) 4 c) 8 d) 16 13
Radiation: example A sphere of radius 0.500 m, temperature 27.0 0 C and emissivity 0.850 is located in an environment of temperature 77.0 0 C. At what rate does the sphere a) emit thermal radiation? b) absorb thermal radiation? c) what is the net rate of energy exchange? Resisting energy transfer 14
Global warming 15