Entropy and the Second Law of Thermodynamics

The incremental change in the entropy (ds) of a unit mass of a system is defined as 

The second law of thermodynamics for a reversible transformation states (in part) that for a reversible transformation there is no change in the entropy of the universe (where universe refers to a system and its surroundings). In other words, if a system receives heat reversibly, the increase in its entropy is exactly equal in magnitude to the decrease in the entropy of its surroundings. 

The concept of reversibility is an abstraction. All natural transformations are, in fact, irreversible. In an irreversible (or spontaneous) transformation a system undergoes finite changes at finite rates, and these changes cannot be reversed simply by changing the surroundings of the system by infinitesimal amounts. 

Exercise 23, Prove that for the same change of state of a system, one carried out reversibly and the other irreversibly 

Solution. In a reversible transformation, state functions of a system (such as pressure) never differ from those of the surroundings by more than an infinitesimal amount. Therefore, 

We define entropy, S, as an additional thermodynamic state function. The infinitesimal change in entropy, dS, is defined as 

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For an isothermal process, the temperature can be taken out of the integral and the integral can be evaluated easily  

Equation 3.14 demonstrates that entropy has units of J/K. These may seem like unusual units, but they are the correct ones. Also, keep in mind that the amount of heat for a process depends on the amount of material, in grams or moles, and so sometimes the unit for entropy becomes J/mol-K. Example 3.2 shows how to include amount in the unit. 

What is the change in entropy when 1.00 g of benzene, CgHg, boils reversibly at its boiling point of 80.1°C and a constant pressure of 1.00 atm The heat of vaporization of benzene is 395 J/g. 

The second law of thermodynamics describes whether a particular energy exchange is possible. Specifically, recall that we previously indicated energy always flows from a higher energy state to a lower energy state. An alternate description would be that energy must always act in a way to iuCTease the microscopic randomness of the system. We use this concept to define a new thermodynamic property called entropy  

There exists a property called entropy, S, which is an intrinsic property of the system, functionally related to the measurable conditions of the system. 

noting that energy must always flow from higher states to lower states, we define the second law of thermodynamics in terms of our definition of entropy  

The entropy change of any system, and its surroundings, considered together, is positive and approaches zero as the process more closely approximates a reversible process. 

This form of the second law can be translated into a mathematical expression describing the entfopy change of a process  

l Consider a three compartment container into which the same particles described in Section 11.3.2 are placed. Calculate the probability of (a) 1 particle being found in the middle compartment, (b) 10 particles, (c) 100 particles. 

2 These particles from Problem Q.lO.l re-sort themselves every picosecond. Assuming that you have a machine to look at the compartments every 10 second, how long would you need to observe the system to find all of the particles in the middle container  

3 An inventor sends a patent application to the Patent office. In it (s)he claims to have found a chemical compound ensures eternal youth for all who drink it. The patent office rejects it on the basis that the formulation is a perpetual motion machine. Explain why. Did they reject it because it was a perpetual motion machine of the first or second kind  

This chapter from The Physical Basis of Biochemistry Solutions Manual to the Second Edition corresponds to Chapter 11 from The Physical Basis of Biochemistry, Second Edition 

5 How much work is done expanding a 10 cm radius cylinder 50 cm against atmospheric pressure (101.325 kPa)  

Curbside recycling programs usually collect comingled materials, as seen here at a Milwaukee site. Plastics, which make up about 85% ofthis pile, must be separated and sorted for recycling. Thomas A. Holme 

After mastering this chapter, you should be able to 

I describe the scientific and economic obstacles to more widespread recycling of plastics. 

I deduce the sign of AS for many chemical reactions by examining the physical state of the reactants and products. 

I state the second law of thermodynamics in words and equations and use it to predict spontaneity. 

Notice that the second law places no limitations on the entropy change of the system or the surroundings either may be negative that is, either system or surroundings may have lower entropy after the process. The law does state, however, that for a spontaneous process, the sum of the entropy changes must be positive. If the entropy of the system decreases, the entropy of the surroundings increases even more to offset the system s decrease, and so the entropy of the universe (system plus surroundings) increases. A quantitative statement of the second law is that, for any real spontaneous process. 

We have seen that processes are spontaneous when they result in an increase in disorder. Nature always moves toward the most probable state available to it. We can state this principle in terms of entropy In any spontaneous process there is always an increase in the entropy of the universe. This is the second law of thermodynamics. Contrast this law with the first law of thermodynamics, which tells us that the energy of the universe is constant. Energy is conserved in the universe, but entropy is not. In fact, the second law can be paraphrased as follows The entropy of the universe is increasing. 

As in Chapter 9, we find it convenient to divide the universe into a system and the surroundings. Thus we can represent the change in the entropy of the universe as 

To predict whether a given process will be spontaneous, we must know the sign of ASuniv. If ASuniv is positive, the entropy of the universe men es, 

Unless otherwise noted, all arton this page is O Cengage Learning 2014. 

Knowing that any spontaneous process is irreversible, can we make predictions about the spontaneity of an unfamiliar process Understanding spontaneity requires us to examine the thermodynamic quantity called entropy, which was first mentioned in Section 13.1. In general, entropy is associated either with the extent of randomness in a system or with the extent to which energy is distributed among the various motions of the molecules of the system. In this section we consider how entropy changes are related to heat transfer and temperature. Our analysis will bring us to a profound statement about spontaneity known as the second law of thermodynamics. 

This sculpture by Picasso in Chicago was allowed to rust to give a pleasing effect. 

The second law of thermodynamics, which we will discuss in this section, provides a way to answer questions about the spontaneity of a reaction. The second law is expressed in terms of a quantity called entropy. 

Let s look at some simple spontaneous processes. Suppose you place a hot cup of coffee on the table. Heat energy from the hot coffee flows slowly to the table and to the air surrounding the cup. In this process, energy spreads out or disperses. The entropy of the system (coffee cup) and its surroundings (table and surrounding air) increases in this spontaneous process. 

Initially, the flask on the left contains a gas, whereas the flask on the right is evacuated.Then, the valve is opened and gas spontaneously flows into the evacuated flask (the vacuum). 

In each of these spontaneous processes, energy has been dispersed or spread out. The entropy of the system plus surroundings has increased. 

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Entropy and the Second Law of Thermodynamics (Frame 2) provide us with a way of deciding whether a given process or reaction is spontaneous. 

Spontaneity, Entropy, and the Second Law of Thermodynamics Free Energy... 

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