Topic: Physics: Statistical Mechanics.

Instructions: Answer the Problems below and Show Complete Solution.

Introductory Statistical Mechanics Problem Sets 1. A sphere of radius 0.450 m, temperature 27.0 C, and emissivity 0.850 is located in an environment of temperature 77.0 C. At what rate does the sphere (a) emit and (b) absorb thermal radiation? (c) What is the sphere's net rate of energy exchange? 2. (a) What is the rate of energy loss in watts per square meter through a glass window 3.0 mm thick if the outside temperature is -29 C and the inside temperature is 22 C? (b) A storm window having the same thickness of glass is installed parallel to the first window, with an air gap of 7.5 cm between the two windows. What now is the rate of energy loss if conduction is the only important energy-loss mechanism? 3. One end of an insulated metal rod is maintained at and the other end is maintained at 100C by an icewater mixture. The rod is 60.0 cm long and has a cross-sectional area of 1.25 cmz. The heat conducted by the rod melts 8.50 g of ice in 15.0 min. Find the thermal conductivity k of the metal. 4. The cross section of a wall made of three layers. The layer thicknesses are L1, L2 = 0.700L1, and L3 = 0.350L1. The thermal conductivities are k1, k2 = 0.900k1, and k3 = 0.800k1. The temperatures at the left side and right side of the wall are TH = 30.0 C and Tc 2 -15.0 C, respectively. Thermal conduction is steady. (a) What is the temperature difference AT; across layer 2 (between the left and right sides of the layer)? If kg were, instead, equal to 1.1k1 (b) Would the rate at which energy is conducted through the wall be greater than, less than, or the same as previously, and (c) What would be the value of ATz? 5. You are asked to design a cylindrical steel rod 50.0 cm long, with a circular cross section, that will conduct 150.0 J/s from a furnace at 450.0C to a container of boiling water under 1 atmosphere. What must the rod's diameter be? 6. A bar of gold (Au) is in thermal contact with a bar of silver (Ag) of the same length and area. One end of the compound bar is maintained at 800C, and the opposite end is at 300C. When the energy transfer reaches steady state, what is the temperature at the junction? 7. Two lightbulbs have cylindrical filaments much greater in length than in diameter. The evacuated bulbs are identical except that one operates at a filament temperature of 2 100C and the other operates at 2 000C. (a) Find the ratio of the power emitted by the hotter lightbulb to that emitted by the cooler lightbulb. (b) With the bulbs operating at the same respective temperatures, the cooler lightbulb is to be altered by making its filament thicker so that it emits the same power as the hotter one. By what factor should the radius ofthis filament be increased