Heat flows to a large block in a
reversible process. What is the
change in the entropy of the
block? Assume its temperature
is constant.
ǻS = (45.0 J)/(285 K)
ǻS = 0.158 J/K
21.5 - Second law of thermodynamics: entropy
Second law of thermodynamics: Entropy
increases, or at best remains constant, in any
isolated system.
If nature abhors a vacuum, as the saying goes, then it revels in messes. The universe
tends toward increasing disorder. So if your life feels like it is becoming increasingly
chaotic, well, you are just going with the flow.
A common non-physicist’s statement of the second law is “systems tend toward
disorder,” a paraphrase of the definition above, which is the second law stated in terms
of entropy. Entropy is considered as a measure of a system’s disorder. The disorder of
a system either stays constant, or increases. Your room never spontaneously becomes
more orderly.
You might think that the second law is violated because you can reduce the entropy of
an object by cooling it. For instance, you can place a hot drink inside a refrigerator and
cool the drink.
However, the second law applies to isolated systems and the refrigerator does not
function as an isolated system. If you place your hand by the back of a refrigerator, you
will realize that refrigerators emit heat. This heat increases the entropy of the
surrounding atmosphere. When we correctly apply the second law to the isolated
system of the refrigerator and surrounding atmosphere, we find that entropy stays
constant, or increases.
A series of reversible processes can, in theory, leave the entropy of a system
unchanged. In practice, however, no process is perfectly reversible, and the entropy of
an isolated system increases as processes occur.
Above, we asserted that the heat flow out of a refrigerator would increase the entropy of
a system. We will show how this is true, using a particular instance.
We rely on the formulation of the second law that states that heat flows spontaneously only from a hotter object to a colder one. Also recall that
the entropy change equals the heat flow divided by the temperature at which the heat flow occurs. The colder the temperature, the larger the
increase in entropy.
In Example 1 on the right, 1100 J of heat flows from an object at 250 K to an object at 130 K. To calculate the system’s entropy change, we
consider the two blocks separately. For the warmer object, we divide the heat by the temperature of the warmer object. Since heat flows out of
the warmer object, that heat flow is negative. The change in entropy of the hotter object is í4.4 J/K. Since heat flows into the cooler object, that
heat flow is positive. Doing similar calculations for the cooler object, but dividing by the cooler object’s lower temperature, we determine that its
entropy change is +8.5 J/K. The net change in entropy for the system is 4.1 J/K. The positive sign for the change in entropy tells us that the
entropy increases and the second law is obeyed.
This example helps to illustrate why entropy increases with spontaneous heat flow. Heat flows from hot to cold, and as the example illustrates,
Entropy and the second law
The entropy of an isolated system can
only increase
The total entropy of the universe is
increasing
Carpe diem