Why is entropy of the universe increasing?

Energy always flows downhill, and this causes an increase of entropy.

Entropy is the spreading out of energy, and energy tends to spread out as much as possible.

It flows spontaneously from a hot (i.e. highly energetic) region to a cold (less energetic) region.

As a result, energy becomes evenly distributed across the two regions, and the temperature of the two regions becomes equal.

The same thing happens on a much larger scale. The Sun and every other star are radiating energy into the universe.

However, they can’t do it forever. Eventually the stars will cool down, and heat will have spread out so much that there won’t be warmer objects and cooler objects.

Everything will be the same very cold temperature.

Once everything is at the same temperature, there’s no reason for anything to change what it’s doing.

The universe will have run down completely, and the entropy of the universe will be as high as it is ever going to get.

If you want to think of it mathematically, consider the total energy #q# that is transferred from a hot region at temperature #T_1# to a cold region at temperature #T_2#.

The entropy #S_1# of the hot region is defined as

#S_1 = q/T_1#

The entropy #S_2# of the cold region is

#S_2 = q/T_2#

Therefore, during the energy transfer, the change in entropy is

#ΔS = S_2 - S_1 = q/T_2 - q/T_1 = q(1/T_2 - 1/T_1)#

Since #T_2 < T_1, 1/T_2 > 1/T_1#, and #ΔS# is positive.

The total entropy of the system increases.

Since energy never flows spontaneously in the other direction, the total entropy of the universe is always increasing.