Thermal Properties of Matter

# Thermal Properties of Matter - Mastering Physics Solutions

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Manage this Assignment: Thermal Properties of Matter Due: 2:00pm on Friday, March 19, 2010 Note: You will receive no credit for late submissions. To learn more, read your instructor's Grading Policy The Speed of Nitrogen Molecules Description: Determine the average speed, root mean square speed, and temperature of a sample of nitrogen gas from a histogram of molecule velocities. One applet based question also. The kinetic theory of gases states that the kinetic energy of a gas is directly proportional to the temperature of the gas. A relationship between the microscopic properties of the gas molecules and the macroscopic properties of the gas can be derived using the following assumptions: The gas is composed of pointlike particles separated by comparatively large distances. The gas molecules are in continual random motion with collisions being perfectly elastic. The gas molecules exert no long-range forces on each other. One of the most important microscopic properties of gas molecules is velocity. There are several different ways to describe statistically the average velocity of a molecule in a gas. The most obvious measure is the average velocity . However, since the molecules in a gas are moving in random directions, the average velocity is approximately zero. Another measure of velocity is , the average squared velocity. Since the square of velocity is always positive, this measure does not average to zero over the entire gas. A third measure is the root-mean-square (rms) speed, , equal to the square root of . The rms speed is a good approximation of the the typical speed of the molecules in a gas. This histogram shows a theoretical distribution of speeds of molecules in a sample of nitrogen ( ) gas. In this problem, you'll use the histogram to compute properties of the gas. Part A What is the average speed of the molecules in the gas? Hint A.1 How to use the histogram The histogram shows the fraction of molecules that have speeds within each of a set of ranges. Each speed range is called a bin . Take the central speed value of each bin as an estimate of the speed of all the molecules in that bin. Compute the weighted average speed, using the percentage of molecules in a bin as the weighting factor for that bin. Hint A.2 More on computing the average MasteringPhysics: Assignment Print View http://session.masteringphysics.com/myct/assignmentPrint?assignmentID=. .. 1 of 18 3/30/2010 9:50 AM

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To find the weighted average, take the average speed of the molecules in each "bin" (for example, the average speed of molecules in the 0-200 range is 100), and multiply that value by the fraction of molecules in that bin. Repeat this process for each bin, adding the results. This will give you the average speed of the molecules in the gas.
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## Thermal Properties of Matter - Mastering Physics Solutions

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