Short Version : 16. Temperature & Heat

16.1. Heat, Temperature & Thermodynamic Equilibrium Thermodynamic equilibrium: State at which macroscopic properties of system remains unchanged over time. Examples of macroscopic properties: L, V, P, , , … 0 th law of thermodynamics: 2 systems in thermodynamic equilibrium with a 3 rd system are themselves in equilibrium. 2 systems are in thermal contact if heating one of them changes the other. Otherwise, they are thermally insulated. Two systems have the same temperature  they are in thermodynamic equilibrium A,B in eqm B,C in eqm  A,C in eqm

Gas Thermometers & the Kelvin Scale Constant volume gas thermometer T  P Kelvin scale: P = 0  0 K = absolute zero Triple point of water  K Triple point: T at which solid, liquid & gas phases co-exist in equilibrium All gases behave similarly as P  0. Mercury fixed at this level by adjusting h  P  T.

Temperature Scales Celsius scale (  C ) : Melting point of ice at P = 1 atm  T C = 0  C. Boiling point of water at P = 1 atm  T C = 100  C.  Triple point of water = 0.01  C Fahrenheit scale (  F ) : Melting point of ice at P = 1 atm  T F = 32  F. Boiling point of water at P = 1 atm  T F = 212  F. Rankine scale (  R ) :

16.2. Heat Capacity & Specific Heat Heat capacity C of a body :  Q = heat transferred to body. Specific heat c = heat capacity per unit mass 1 calorie (15  C cal) = heat needed to raise 1 g of water from 14.5  C to 15.5  C. 1 BTU (59  F) = heat needed to raise 1 lb of water from 58.5  F to 59.5  F.

c = c(P,V) for gases  c P, c V.

The Equilibrium Temperature Heat flows from hot to cold objects until a common equilibrium temperature is reached. For 2 objects insulated from their surroundings: When the equilibrium temperature T is reached: 

16.3. Heat Transfer Common heat-transfer mechanisms: Conduction Convection Radiation

Conduction Conduction: heat transfer through direct physical contact. Mechanism: molecular collision. Thermal conductivity k, [ k ] = W / m  K Heat flow H, [ H ] = watt :

conductor insulator

Specific Heat vs Thermal Conductivity c ( J/kg  K )k (W/m  K ) Al Cu Fe Steel50246 Concrete8801 Glass Water Wood

applies only when T = const over each (planar) surface For complicated surface, useProb. 72 & 78. Composite slab: H must be the same in both slabs to prevent accumulated heat at interface Thermal resistance :[ R ] = K / W   Resistance in series

Insulating properties of building materials are described by the R-factor ( R-value ). = thermal resistance of a slab of unit area U.S.

Example Cost of Oil The walls of a house consist of plaster ( R = 0.17 ), R-11 fiberglass insulation, plywood (R = 0.65 ), and cedar shingles (R = 0.55 ). The roof is the same except it uses R-30 fiberglass insulation. In winter, average T outdoor is 20  F, while the house is at 70  F. The house’s furnace produces 100,000 BTU for every gallon of oil, which costs $2.20 per gallon. How much is the monthly cost?

Convection Convection = heat transfer by fluid motion T      rises Convection cells in liquid film between glass plates (Rayleigh-Bénard convection, Benard cells)

Radiation Glow of a stove burner  it loses energy by radiation Stefan-Boltzmann law for radiated power:  = Stefan-Boltzmann constant = 5.67  10  8 W / m 2 K 4. A = area of emitting surface. 0 < e < 1 is the emissivity ( effectiveness in emitting radiation ). e = 1  perfect emitter & absorber ( black body ). Black objects are good emitters & absorbers. Shiny objects are poor emitters & absorbers.

Wien‘s displacement law : max = b / T  P  T 4  Radiation dominates at high T. Wavelength of peak radiation becomes shorter as T increases. Sun ~ visible light. Near room T ~ infrared. Stefan-Boltzmann law :

Example Sun’s Temperature The sun radiates energy at the rate P = 3.9  W, & its radius is 7.0  10 8 m. Treating it as a blackbody ( e = 1 ), find its surface temperature.  = 5.67  10  8 W / m 2 K 4

Conceptual Example Energy-Saving Windows Why do double-pane windows reduce heat loss greatly compared with single-paned windows? Why is a window’s R-factor higher if the spacing between panes is small? And why do the best windows have “low-E” coatings? Thermal conductivity (see Table 16.2): Glassk ~ 0.8 W/m  K Airk ~ W/m  K  Layer of air reduces heat loss greatly & increases the R -factor. This is so unless air layer is so thick that convection current develops. “low-E” means low emissivity, which reduces energy loss by radiation.

Making the Connection Compare the for a single pane window made from 3.0-mm-thick glass with that of a double-pane window make from the same glass with a 5.0-mm air gap between panes. Glassk ~ 0.8 W/m  K Airk ~ W/m  K

16.4. Thermal Energy Balance A house in thermal-energy balance. System with fixed rate of energy input tends toward an energy- balanced state due to negative feedback. Heat from furnace balances losses thru roofs & walls

Example Solar Greenhouse A solar greenhouse has 300 ft 2 of opaque R-30 walls, & 250 ft 2 of R-1.8 double-pane glass that admits solar energy at the rate of 40 BTU / h / ft 2. Find the greenhouse temperature on a day when outdoor temperature is 15  F.

Application: Greenhouse Effect & Global Warming Average power from sun : Total power from sun : Power radiated (peak at IR) from Earth :  C.f.  T   15  C natural greenhouse effect Greenhouse gases: H 2 O, CO 2, CH 4, … passes incoming sunlight, absorbs outgoing IR. Mars: none Venus: huge

CO 2 increased by 36% 0.6  C increase during 20 th century. 1.5  C – 6  C increase by 2100.