Entropy

Overview

Source: Ketron Mitchell-Wynne, PhD, Asantha Cooray, PhD, Department of Physics & Astronomy, School of Physical Sciences, University of California, Irvine, CA

The second law of thermodynamics is a fundamental law of nature. It states that the entropy of a system always increases over time or remains constant in ideal cases when a system is in a steady state or undergoing a "reversible process." If the system is undergoing an irreversible process, the entropy of the system will always increase. This means that the change in entropy, ΔS, is always greater than or equal to zero. The entropy of a system is a measure of the number of microscopic configurations the system can attain. For example, gas in a container with known volume, pressure, and temperature can have an enormous number of possible configurations of the individual gas molecules. If the container is opened, the gas molecules escape and the number of configurations increases dramatically, essentially approaching infinity. When the container is opened, the entropy is said to increase. Therefore, entropy can be considered a measure of the "disorder" of a system.

Procedure

1. Setup.

Obtain a heating element and stand, a thermometer, a stopwatch, a few paper towels, water, and a large beaker.
Fill the beaker with enough water so that the sample will not cool down too rapidly (i.e., at least 500 mL).
Place the beaker full of water on the stand below the heating element and turn it on.
Once the beaker of water reaches a boil, insert the thermometer and turn off the heating element.
Carefully remove the beaker from the heating stand

Results

Representative results for 680 mL of water are shown in Table 1. The cooling constant k was found using the data points in the table and solving Equation 7. After 35 min, T(35) = 50.6. The initial temperature was 100 °C, and data collection ceased at 28.5 °C. Using these variables gives the following equation to obtain k:

50.6 = 28.5 + (100 - 28.5)

Application and Summary

A pair of headphones kept in a bag always tends to become knotted-this is an increase in entropy caused by carrying the bag around. It is necessary to do work on the headphones to un-knot them and decrease the entropy (this can be thought of as a "reversible process"). The most efficient heat engine cycle allowed by physical laws is the Carnot cycle. The second law states that not all heat supplied to a heat engine can be used to do work. The Carnot efficiency sets the limiting value on the fraction of heat that can be u