# Entropy Change for an Isolated System

This is called the

.
Consider the

#### isolated system

, shown here.
Recall from Chapter 1 that no mass or energy crosses the boundary of an isolated system.
Therefore, an

0
because:

#### Isolated closed system

The universe is an isolated system.
Therefore, we can conclude that:
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### Ch 7, Lesson C, Page 6 - Entropy Change for an Isolated System

• Do you remember what an isolated system is ?
• An isolated system is one that is both closed and adiabatic.
• So, when an isolated system undergoes a process, what is the change in entropy of the system ?
• We can answer this by using the defining equation for entropy generation.
• Since the system is adiabatic, Q is zero and so is dQ.
• That simplifies the problem a great deal because we don’t need to figure out how to evaluate the integral.
• We are left with ΔS for the isolated system is equal to Sgen.
• So, since we know Sgen can only be positive, ΔS for the isolated system must also be strictly positive.
• Now, for the cool part.
• If we assume that there is nothing outside of our universe, then the universe is an isolated system.
• This lets us make the big conclusion.
• The entropy of the universe cannot decrease.  This is the Principle of Increasing Entropy and it is a consequence of the 2nd Law.
• Let me say it again.  The entropy of the universe cannot decrease.  This is actually another statement of the 2nd Law.
• For isolated systems, ΔS = 0 for reversible processes and ΔS  > 0 for irreversible processes.
• So, if no heat transfer occurs during a process that takes place in a closed system, the increase in the entropy of the system is due completely to the irreversibility of the process.
• Once again ΔS is tied in to the irreversibility of a process.