Mechanical Equivalent of Heat

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1 Ch 14 Heat

2 What is heat? Heat is energy that moves from an object at a higher temperature to an object of lower temp. Heat was originally described as movement of a fluid substance called caloric.

3 Mechanical Equivalent of Heat James Prescott Joule performed experiments to show how heat, like work, transfers energy. Joule found that a given amount of work done was always equal to the same amount of heat input J = 1 cal x 10 3 J = 1 kcal

4 Units of Heat Energy Units include calorie (cal)- amount of heat necessary to raise the temp of 1g of water 1 C Kilocalorie (kcal) calories or same definition as above for 1 kg of water by 1 C (also called the Calorie (C) as in energy content of food. British Thermal Unit (Btu)- heat needed to raise 1 lb of water 1 F 1 Btu = kcal = 1055 Joules

5 Heat transfer as Energy Heat transfer came to be understood as a transfer of energy from a hot object to a cooler one. SI unit for heat is the Joule. (Energy) KE is an indication of heat content of a material. If work is done on an object, its KE and temp increase. Vice versa holds true for cooling.

6 Example 14-2 When a 3.0g bullet, traveling at 400m/s passes through a tree its speed is reduced to 200m/s. How much heat Q is produced and shared by the bullet and tree? Solution: Energy conservation says Ke i = Ke f + Q so Q 1 2 m(v i2 v f 2 ) 1 2 (3.0x10 3 kg) 400m /s 2 200m /s 2 180J 180J 4.186J /cal 43cal This is distributed between the bullet and the tree according to each of the materials abilities to transmit and store heat energy.

7 Temp, Heat, & Internal Energy Thermal energy or internal energy is the sum total energy of all molecules in an object. Heat is the amount of energy transferred from one object to another at a different temperature. Temperature (in Kelvin) is a measure of the average kinetic energy of individual molecules. Two chunks of iron may have the same temperature but if one has twice the mass, it has twice the thermal energy as the other.

8 Internal Energy of a gas Internal Energy, U, of an ideal gas depends only on the temperature and number of moles of gas. U 1 2 (mv 2 ) U 3 2 NkT U 3 2 nrt N is the total number of molecules n is the number of moles

9 Specific Heat Q=mcΔT If heat is put into an object, its temperature increases how much depends on the mass, type of material, (its ability to hold heat content), and the temperature difference. Specific Heat, c, of a material is the energy required to raise 1kg of a material s temp 1 C. Units for c are kcal/kg C or J/kg C For water at 15 C, c = 1.00 kcal/kg C or 4.19x10 3 J/kg C Air heats up faster than water on a sunny day due to a lower specific heat, c, than water s. See table 14-2.

10 Latent Heat During a phase change, heat is added (or removed) and a certain amount of energy is required Heat of Fusion is the energy required for a phase change from solid to liquid, L F. For water L F is 79.7 kcal/kg or 333kJ/kg. Heat of Vaporization is the energy required for a phase change from liquid to gas, L V. For water L V is 539 kcal/kg or 2260kJ/kg.

11 Latent Heat Diagram Energy moves both directions. The same amount of energy is required or released as phase changes occur. Latent heat is the value for the heat of fusion or vaporization, L. The total heat involved during a phase change depends on the latent heat, L and on the total mass of the substance: Q = ml. (Q is the heat required or given off during the phase change.

12 Heat Transfer: Conduction Conduction is transfer of thermal energy by collisions between molecules at different temperatures. (Objects in contact with ΔT). Rate of heat flow by conduction depends on temperature difference and size and shape of objects. Q where A is cross-sectional area, l is distance between two ends, and k is proportionality constant, thermal conductivity. If k is large, substances conduct heat rapidly and are good conductors. See table T kat T 2 1 l

13 Ex 14-11: Heat loss through 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 temps at the inner and outer surfaces are 15.0 C and 14.0 C respectively.

14 Ex Solution Since A = (2.0 m)(1.5 m) = 3.0 m 2, l= 3.2 x 10-3 m and we get k from the table, so Q T kat 1 T 2 l 790J /s (0.84J /s m C )(3.0m2 )(15.0 C 14.0 C) (3.2x10 3 m) (790J /s)(4.19x10 3 J /kcal) 0.19kcal/s 680kcal/h Double pane windows increase the air layer thickness to reduce heat loss more than a single pane of glass, since the thermal conductivity of air is much less than that for glass.

15 Insulators Clothing helps keep us warm by trapping air around our bodies so it cannot move and be replaced by colder air. (So it s not the cloth that keeps us warm, but the air we trap). Materials like down and thermals fluff air and trap them around our bodies to prevent loss of heat by conduction. (What if feathers get wet?) Insulating materials are specified by R-values depending on k and thickness, l. R=l/k. Higher R values are better insulators.

16 Heat Transfer: Convection Heat transfer by movement of molecules over long distances. This usually happens in gases and liquids and is called Convection currents. As air or water is heated, it expands. Less dense material rises. Warmer materials rise and cooler materials sink. This gives inland day breezes and outland evening breezes near lakes / beaches.

17 Heat Transfer: Radiation While conduction and convection require a medium to carry heat from hot to cold matter, radiation requires NO medium. Radiation travels through empty space by EM waves (heat is IR). Objects radiate heat at a rate proportional to their Kelvin temperature to the 4 th power and their surface area, A.

18 Radiation cont d The Stefan-Boltzmann equation gives the rate of heat radiation by: Q T e AT 4 Here e is the emissivity (a # between 0 and 1 like black substances are close to 1 and shiny stuff is close to 0 radiation), and σ is the Stefan-Boltzmann constant, 5.67 x 10-8 W/m 2 *K 4 Shiny surface neither absorb nor emit much radiation. A good absorber, like dark objects, is also a good emitter.

19 Solar Radiation Although the Sun s energy travels to Earth by radiant waves, heating by the Sun is calculated considering about 1350J of energy strike the atmosphere of Earth per second per square meter at right angles to the Sun s rays. 1350W/m 2 is called the Solar constant. Our atmosphere absorbs about 70% of the Sun s energy so we tend to receive about 1000W/m 2.

20 Earth s axis and seasons An object of emissivity, e, with area A facing the sun absorbs heat at a rate of Q T (1000W /m2 )ea cos

21 Your turn to Practice Please do Ch 14 Rev pgs #s 1, 2, 15, 16, 30, 33, 35, 39, and 40.

Chapter 18 Temperature, Heat, and the First Law of Thermodynamics. Problems: 8, 11, 13, 17, 21, 27, 29, 37, 39, 41, 47, 51, 57

Chapter 18 Temperature, Heat, and the First Law of Thermodynamics Problems: 8, 11, 13, 17, 21, 27, 29, 37, 39, 41, 47, 51, 57 Thermodynamics study and application of thermal energy temperature quantity