Physics 2 – April 6, 2017 Do Now – get out 8.1 homework for two homework checks. (can’t find sub lists) Revisit last class materials. Time for homework assignment. Will check tomorrow. Ch 8.2 p338 #26-38 Answers available to check as you go. Review worksheet tomorrow. I will post answers by Sunday, 5 pm and you can get further help on Monday if needed.

Homework Answer Photos

Homework Answer Photos

Homework Answer Photos

Homework Answer Photos

Homework Answer Photos

Homework Answer Photos

Homework Answer Photos

Objectives/Agenda/Assignment 8.2 Thermal Energy Transfer Assignment: p338 #26-41 Agenda: Types of Thermal Energy Transfer Black Body Radiation Solar Radiation Albedo and Energy Balance Greenhouse Effect

Types of Thermal Energy Transfer When two bodies at different temperatures are next to one another, they are not in thermal equilibrium and energy transfer will flow from the hot body to the cold body according to the second law of thermodynamics. Three mechanisms for transferring: Conduction (Requires contact) Convection (Requires contact) Radiation (Occurs over space)

Conduction Particle movement transfers energy from the direct collision of particles in the hot with particles in the cold The rate of transfer of energy Q/  t Depends….. Directly on the surface area of contact, A (Faster when interface is greater) Indirectly on the distance the temperature difference spans, L (Takes longer to go farther) Directly on the temperature difference T (The greater the difference, the faster it goes) The proportionality constant is k Put together these effects and 𝚫𝑸 𝚫𝒕 =𝒌𝑨 𝚫𝑻 𝑳 Note: mc*T/t=kA/L*T T/t  T Compare to dx/dt =k x When a rate is proportional to the variable, this is called a first order differential equation. We will see this equation several times: with nuclear decay and capacitance too. We’ll skip the math here.

Convection Recall from the kinetic theory of gases that as a gas (a type of fluid) increases in temperature, the volume increases, decreasing the fluid density causing a hot sample to rise relative to a cold sample. This relative motion of hot rising relative to cold creates convection currents that serve to transfer heat away from the contact surface, increasing the rate of thermal energy transfer by conduction alone. Only happens for fluid (liquid or gas) objects. IB only treats this mechanism qualitatively.

Radiation (Black body) Because all matter is at some temperature above absolute zero, there is a thermal transfer of energy from any given object to its surroundings To simplify the model, we assume that the surroundings have 0 K even though this is just ideal. The Stefan-Boltzmann law describes the rate of thermal energy radiation (P = Q/  t) 𝑷=𝒆𝝈𝑨 𝑻 𝟒 where e is the emissivity (1 for an ideal emitter – see table)  is the Stefan-Boltzmann constant = 5.67 x 10-8 W/m2K4 (in data booklet) A is the surface area of the object (A = 4r2 for a spherical object)

Wien’s displacement law The black body radiation power intensity (Power divided by area) varies over a range energies, just like we had a distribution of particle energies according to the Boltzmann distribution in Ch 3.2. Notice that the wavelength for the highest peak (drop perpendiculars) decreases as the temperature increases. It is an indirect proportionality max  1/T Or max T = 2.90 x 10-3K m which is Wien’s Law

Solar radiation The thermal power of the sun (the rate of energy production of its nuclear fission reactions) is P = 3.9 x 1026 W The intensity of the sun’s radiation at the location of earth (that is at a distance of 1.5 x 1011 m = the earth – sun distance) is given by 𝑰= 𝑷 𝟒𝝅 𝒅 𝟐 Recall radiation intensity is power over surface area Result is the intensity of the sun at the earth, S = 1360 W/m2 and is called the solar constant (Listed as a constant in the data booklet)

Intensity of sun on earth surface Recall I = P/A or to rearrange P = IA At the surface of the earth (with a radius R) P = SR2 We only receive the energy cut by the disc of A = R2 The intensity at the surface is the P/A for the surface area of the earth 4R2 So I = S/4 But this neglects the energy reradiated by the earth because it is also a black body radiator. This effect is described by the concept of albedo

Albedo Albedo is the ration of the total scattered power (reradiated) to the total incident power (portion of S we receive through our shadow disc) Given the symbol  and ranges from 0 (perfect absorber) to 1 (perfect reflector) Albedo varies over the surface of the earth from charcoal (0.04) to snow (0.85) Average albedo for the earth  = 0.3. So only 70% or (1 – ) of the intensity of the sun (S/4) that reaches the earth is delivered. 𝑰 𝒂𝒗𝒆 = 𝟏−𝜶 𝑺 𝟒 =𝟐𝟒𝟓 𝑾/ 𝒎 𝟐

Greenhouse Effect If we assume all radiation that is reradiated reaches space we calculate the average temperature of the earth to be -17C when we observe it to be 15C. The 32C difference reflect the amount of heat trapped by our atmosphere. Greenhouse gases include water, carbon dioxide, methane and nitrous oxide. There are both natural and manmade (anthropogenic) sources of these greenhouse gases.

Exit Slip - Assignment Exit Slip- none What’s Due on Apr 7? (Pending assignments to complete.) Ch 8.2 p338 #26-38 What’s Next? (How to prepare for the next day) Start studying for the Thermodynamics test on April 11 (Tentative)