Trying to better understand temperature and entropy

[Jaccobtw]

TL;DR

From my understanding, we can think of entropy as how spread out energy is within a system. The more spread out, the more entropy. The more condensed, the less entropy.

If you were to condense all the energy in the universe into a point, wouldn't the temperature be very high, yet the entropy be very low? Also if you were to spread out all of the energy in the universe, wouldn't the temperature be near zero and the entropy be very high? And this makes entropy units - J/K - make sense. Because the total amount of energy in the universe is constant (2nd Law Thermodynamics), yet the average energy (temperature) seems to decrease, this would mean that the entropy of the universe can only net increase. Is this a correct understanding of entropy or am I off? Thanks for your help.

 

[Demystifier]

If you were to condense all the energy in the universe into a point, wouldn't the temperature be very high, yet the entropy be very low?

Temperature at that point would be very high, but everywhere else it would be zero. The entropy density at that point would be very high, but everywhere else the entropy density would be zero. The entropy, that is entropy density integrated over whole universe, would therefore be low.

In thermodynamics it's very important to distinguish extensive quantities from intensive quantities. Extensive quantities increase with the size of the system, examples are entropy and energy. Intensive quantities do not increase with the size of the system, examples are temperature, pressure, entropy density and energy density. In fact, all intensive quantities can be understood as kinds of "densities". Pressure is a "density" of force (but force per area, not force per volume), while temperature is related to the energy density (but the exact relation, in general, is not so simple).