These principles can be stated in terms of a system and its environment. With an irreversible process, a system can be returned to its initial

state but its environment must change. This is particularly applicable to heat engines, where the “environment” may be modeled as hot and

cold reservoirs. The engine mechanism, the gas and the piston, can be returned to their initial state, but their environment changes. The hot

reservoir becomes a little less hot and the cold reservoir becomes warmer each time the engine completes a cycle.

21.4 - Entropy

Entropy: A property of a system. When heat is

transferred to a system, its entropy increases.

Entropy is a concept used to describe the state of a system, and it is a property of a

system, just like pressure, volume, temperature or internal energy. Some properties

may be directly measured or read from a gauge. A thermometer will tell you an object’s

temperature and a meter stick will tell you its length. For other properties, such as

kinetic energy, there are no direct measures; there are no “KE gauges.” A property like

kinetic energy must be computed from factors that can be measured, mass and speed.

Similarly, there are no direct “entropy gauges” available to scientists or students. In this

section, we focus on the relationship of entropy, temperature and heat without

concerning ourselves too much about exactly what is meant by “entropy.” In other

words, we will start our discussion of entropy by considering some properties that can

be observed and are familiar to you, and focus on entropy itself once this groundwork

has been laid. In fact, the concept of entropy was historically developed in a process

like this. It arose out of the quest to understand the relationship between temperature

and heat.

When heat flows into a system, its entropy increases. When heat flows out of a system,

its entropy decreases. The change in entropy equals the heat divided by the

temperature at which the heat flow occurs.

We express this as a formula in Equation 1. To apply this equation, the process must be

reversible and the temperature measured in kelvins. Since absorbing or expelling heat

will change the temperature of the system, this change in entropy must be measured for

a small amount of heat, or the system must be large enough that it can expel or absorb

a fair amount of heat with only a negligible change in temperature. The units for entropy

are joules/kelvin.

This equation is useful for two reasons. First, it provides the tool for computing a

change in entropy. Second, it (finally!) provides a definition of temperature more formal

than just “something measured by a thermometer”: Temperature is the slope of an

entropy-heat curve. (Solving the equation on the right for temperature shows why this is

the case.)

The entropy of a system, like any property, depends only on the system's state, not how

the system arrived there. There are many processes that change a system from a

particular initial state to a particular final state. The system’s resulting change in entropy

is the same for any of these processes. (This is analogous to gravitational potential

energy, where only the initial and final positions of an object matter, not the path it took

between them.)

At the right, you see a graph of temperature plotted against entropy. As heat flows into

an object, its temperature increases, as does its entropy. The area under the curve,

positive or negative, equals the amount of heat transferred.

The curve is not a straight line. The horizontal section occurs at a first-order phase transition, where heat added causes the substance to

change from solid to liquid, or liquid to gas. At phase transitions, adding heat increases the entropy, but not the temperature.

Entropy

Property of objects, systems

Increases as heat is transferred to

object

ǻS = change in entropy

Qrev = net heat transferred in reversible

process

T = temperature (K)

Units: joules/kelvin (J/K)

(^386) Copyright 2007 Kinetic Books Co. Chapter 21