For an ideal gas, the internal heat content of the gas is proportional to the temperature T of the gas. In particular for a monatomic gas, U = 3/2 NkT.

If a quantity of heat Q is added to any substance, then one might expect the heat energy content of that substance to increase and thus increase the substance's temperature. This does not always happen. For example, during the melting of ice (or any phase change) the temperature remains constant while heat is being added.

If the added heat does not raise the temperature, what has happened to the energy added? For the melting of ice, the added energy has gone into destroying the orderly arrangement of the atoms and turning the crystal-ice into a less orderly arrangement of liquid-water.

How could we construct a quantity that would measure whether the energy added to a substance is going into thermal energy or into destroying order? Conversely, how could we construct a quantity that would measure whether the energy removed from a substance goes into lowering the substance's thermal energy content or into creating a more ordered structure.

One such quantity that would - in my opinion - have been a better definition of entropy would be

Instead of ΔS = Q/T.

This would make the units of entropy dimensionless and the change in entropy could be thought of as simply being equal to the ratio of Heat Energy Absorbed over the Thermal Energy. If a substance absorbs heat and doesn't change its temperature, then this ratio gets bigger positively and its entropy/disorder increases. If a substance loses heat and doesn't change its temperature, then this ratio gets smaller negatively and its entropy/disorder decreases.