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Unformatted text preview: Aerogel – an excellent thermal insulator known as frozen smoke • When heated, a solid material experiences an increase in temperature signifying energy has been absorbed; Energy content depends on: – Temperature – The material Heat Capacity: – A materials ability to absorb heat from its external surroundings – Amount of energy required to produce a unit temperature rise – In mathematical terms, • dQ C dT where dQ is the energy required to produce a dT temperature change. – C represents energy needed to raise one mole of a solid by one degree J/mol‐K . • • •
v – p • In solid materials, atoms are constantly vibrating at high frequencies and small amplitudes • Elastic/ sound waves: – Short wavelength – High frequency – Propagate through crystal at the speed of sound
Schematic representation of the generation of lattice waves in a crystal by means of atomic vibrations • Many traveling lattice waves are produced, with a range of distributions and frequencies • • •
– – • Heat capacity is sensitive to temperature.
Gas constant, R The temperature dependence of the heat capacity at constant volume Debye temperature, D ; usually less than Troom • At low T D Cv AT3 Temperature dependent • At high T D Cv 3R ‐‐‐ 25 J/mol‐K Temperature independent •
– • l l T l0
‐1 OR l f l0 l0 l (l f l0 )
Linear coefficient of thermal expansion • V v T V0
v Volume coefficient of thermal expansion v 3 l • • Thermal expansion is reflected at the atomic level by an increase in the average distance between the atoms Best understood by the viewing the potential energy‐versus‐ interatomic spacing curve for a solid material Chapter 2 Increasing trough width with rising temperature Average vibrational amplitude of an atom • Thermal expansion is due to the asymmetric curvature of this potential energy trough NOT the increased atomic vibrational amplitudes with rising temperature • A potential energy curve that is symmetric would correspond to no net change in interatomic separation and therefore NO thermal expansion
Trough width does not increase with rising temperature al
Material Polymers Polyproylene Polyethylene Polystyrene Teflon Metals Aluminum Steel Tungsten Gold Ceramics Magnesia (MgO) Alumina (Al2O3) Soda-lime Glass Silica (crytslline SiO2)
12 α (10-6 / K) at room temp 145 – 180 106 – 198 90 – 150 126 - 216 23.6 12 4.5 14.2 13.5 7.6 9 0.4 Increasing α http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/jarlid.html •
– • Put it in the freezer for a while. 13 • Expansion can lead to severe distortion.
– Welded railway tracks • Differential expansion can be used as heat sensor and actuator http://www.howstuffworks.com/home-thermostat1.htm http://structures-www.cv.ic.ac.uk/examples/
– – l • • Heat Flux, Units: W/m2 dT q k dx
Thermal conductivity, Units: W/m‐K Temperature gradient through the conducting medium •
– – • • • • • • E l (T0 T f ) E l T • • •
19 Re-entry T Distribution Space Shuttle Orbiter Fig. 23.0, Callister 5e. (Fig. 23.0 courtesy the National Aeronautics and Space Administration. reinf C-C (1650°C) silica tiles (400-1260°C) nylon felt, silicon rubber coating (400°C) • Silica tiles (400-1260 C) Large scale application Fig. 19.2W, Callister 6e. (Fig. 19.2W adapted from L.J. Korb, C.A. Morant, R.M. Calland, and C.S. Thatcher, "The Shuttle Orbiter Thermal Protection System", Ceramic Bulletin, No. 11, Nov. 1981, p. 1189.) Microstructure:
~90% porosity! Si fibers bonded to one another during heat treatment. 100 m
Fig. 19.3W, Callister 5e. (Fig. 19.3W courtesy the National Aeronautics and Space Administration. 20 Fig. 19.4W, Callister 5e. (Fig. 219.4W courtesy Lockheed Aerospace Ceramics Systems, Sunnyvale, CA.) • • • • • •
21 1. A 2 mm thick glass sheet is being used for a window. The thermal conductivity of glass is 1.7 J/ m.K.s . The temperature outside is ‐20°C and that inside is 20°C. Assuming steady‐state is reached, how far into the glass sheet, from the high temperature side, will the temperature be 15°C. a b c d e 0.25 mm 0.50 mm 0.75 mm 1.00 mm 1.25 mm ‐8 ‐ 8 ‐8 ‐3 ‐4 ‐5 ‐5 4. Consider the figure below, which shows the inter‐atomic potential, U, vs. the interatomic distance, r, for a metal. Which of the following statements is most correct? 0 0 0 0 ...
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This note was uploaded on 02/17/2011 for the course ENGINEERIN 1m03 taught by Professor Porove during the Spring '10 term at McMaster University.
- Spring '10