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3.6

# Entropy is not conserved

Entropy
• Unlike energy functions, entropy is not conserved in natural process or in isolated systems.
• For example, consider heat transfer between two objects with different temperature TI and TII (TI > TI)in an isolated system. The two objects are connected by a thermal conductor such as a copper wire. The heat will flow from the high temperature side (I) to the low temperature side (II). Assuming no heat loss, the heat from I will go into II, thus $Q$$I$=−$Q$$II$

• The internal energy change of the whole system (I+II) is thus zero.
$U$$I+II$=$∆U$$I$+$∆U$$II$=$Q$$I$+$Q$$II$=0
The energy is conserved.
• Let’s consider the entropy change of the whole system (I+II).

Insert the relation $Q$$I$=−$Q$$II$

The entropy of this isolated system is not conserved. This heat flow is spontaneous and irreversible and the irreversibility cause entropy increase.