MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics Physics 8.01T Fall Term 2004 Problem Set 12: Kinetic Theory; Mechanical Equivalent of Heat; Available on-line November 19; Due: Friday December 3 at 4:00 p.m.Please write your name, subject, lecture section, table, and the name of the recitation instructor on the top right corner of the first page of your homework solutions. Please place your solutions in your lecture section table box. Nov 19 No Class Problem Set 11: Due Tues Nov 23 at 4:00 pm. Nov 22 Hour One: Kinetic Theory Reading: YF 18.1-18.6 Hour Two: Problem Solving Session 18: Ideal Gas Law Reading: YF 18.1-18.6 Nov 24 Hour One: Archimedes Principle Reading: YF 14.1-14.3 Hour Two: Archimedes Principle PRS Contest Nov 26 No Class Problem Set 12: Due Fri Dec 3 at 4:00 pm. Nov 29 Hour One: First Law of Thermodynamcics, Entropy, and Second Law of Thermodynamics Hour Two: Problem Solving Session 19: Thermodynamics Dec 1 Hour One: Temperature, Heat, and Heat Capacity Reading: YF 18.4: YF 17.1-17.7 Hour Two: Experiment 10: Energy Transformations: Mechanical Equivalent of Heat Reading: Experiment 10Dec 3 Hour One: Problem Solving Session 20: First and Second Thermodynamics Problem Set 13: Not graded. Recommended Final Review Discussed in class Dec 8 Dec 6 Hour One: Special Relativity: Space-Time, Causality and Simultaneity Reading: YF: Chapter 37.1-37.4 p. 1403-1414 Hour Two: Problem Solving Session 21: Special Relativity: Time Dilation and Length Contraction Dec 8 Hour One and Hour Two: Final Review Final Exam Tuesday, December 14 9:00AM - 12:00 NOONProblem 1: Isothermal Ideal Gas Atmosphere a) Find the root mean square (rms) speed of an oxygen molecule at T = 300K at sea level. b) Find the root mean square z-component of the velocity of an oxygen molecule at T = 300K at sea level. c) If a molecule with the above z-velocity were in a large evacuated container, to what maximum height H would it rise? d) Find the rms z-component of velocity of a nitrogen molecule at T = 300K and height H assuming that the atmosphere extends that high (which it does)? Problem 2: Measuring Speeds of Gas Molecules The actual speeds of atoms and molecules were first measured directly in 1930 by the following experiment. A beam of bismuth atoms, evaporated from an ‘oven’, passed through some defining slits in a hollow cylinder of 2radius R = 4.7 ×10−2 m , rotating with frequency f = 1.2 ×10 Hz . The cylinder had a narrow slit cut in one side parallel to its axis. A glass plate was mounted opposite the slit in the cylinder. (See sketch). The fastest atoms would arrive at the leading edge of the plate and the slower atoms would distribute themselves further back along the plate. The following graph shows the results for Bismuth atoms at a temperature T = 827 0C . In this problem we shall calculate the velocity of the Bismuth atoms at the maximum of the distribution curve. The Bismuth atoms have a molecular weight M = 2.09 ×102 g mole . a) What is the displacement backwards along the glass of the maximum of the curve? b) What angle (in radians) does this correspond to?c) How long does it take for the cylinder to rotate through this angle? (This corresponds to the time it takes the Bismuth atom to cross the diameter of the cylinder). d) What is the velocity of these Bismuth atoms? e) Using the equipartition theorem v2 = 3RT M , where the universal gasrmsconstant R = 8.31 Jmole − K , calculate the root mean square velocity of the Bismuth atoms. How does your answer compare to part d)? Problem 3: Burning Calories A racing bicyclist, traveling at an average speed of 25 mph, has a metabolic rate of 3dE / dt = 1.36 ×10 W. The average power output is dW / dt = 3.0 ×102 W . The person cycles for 4 hours and covers 100 miles. The person has mass m = 60 kg. a) What is the average force that the person applies? b) What is the ratio of power output to catabolic rate, ε= dW / dt ?dE / dt c) How many kilocalories did the person burn up? d) What rate did the cyclist generate heat? e) What happens to this heat? Problem 4: Experiment Mechanical Equivalent of Heat This problem will be part of the experiment write-up (last page) and given out in class the day of the experiment. Problem 5: Hand in the In-class problem Friday Dec 3 with your problem
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