The law that supplies a direction

State it carefully:

$$\Delta S_{\text{total}} \ge 0 \quad \text{for an ISOLATED system}, \qquad \Delta S = \frac{Q}{T}.$$

A system that trades energy with its surroundings has no such restriction. Water freezing in a freezer becomes more ordered and its entropy falls. A crystal growing from solution does the same. So does a gas being compressed. None of these breaks anything, because in each case the surroundings gain more entropy than the system lost.

The refrigerator is the standard demonstration. It lowers the entropy of the food; it warms the kitchen by more than enough to pay for that; and it consumes electrical energy to do so. Draw the boundary around the kitchen and the total has gone up. Draw the boundary before applying the law, and ask what that boundary encloses.

A block slides across a floor and stops. Where did its $20$ J of kinetic energy go? Into internal energy of the block and the floor, spread across an enormous number of particles. Every joule is accounted for, which is the first law doing its job.

What changed is availability. Concentrated in one moving block, that energy could lift a weight. Dispersed among $10^{24}$ particles that are all at nearly one temperature, nothing gathers it back. Entropy is the measure of that spreading, it has its own units of J/K, and it is not a quantity of joules.

Two sentences worth deleting from your vocabulary: "friction destroyed the energy" and "the entropy increase is $20$ J". The first contradicts the first law. The second confuses two different quantities with two different units.

Consider energy leaving a cool room and entering a hot cup of coffee. The books balance exactly: the room's loss equals the coffee's gain. The first law has no objection at all, and yet nobody has ever seen it.

The reason is statistical. Energy concentrated in one place has vastly more ways to be spread out than to stay concentrated, so an isolated system drifts toward its most probable arrangement, which is thermal equilibrium at maximum entropy. Reversing that means finding one particular arrangement out of an unimaginable number, and the odds are not small so much as unreachable.

So a process has to clear two tests, not one:

1. First law. Do the energy totals match?
2. Second law. Does the entropy of the isolated system fail to decrease?

Checking only the first is what makes a perpetual-motion proposal look plausible on paper.

The second law has a consequence worth naming, because it explains a number students often find arbitrary. A heat engine takes energy from a hot reservoir, converts part of it to work, and dumps the rest into a cold reservoir. It cannot convert all of it.

The reason is the entropy ledger. Drawing $Q_H$ out of the hot reservoir lowers its entropy by $Q_H/T_H$. Work carries no entropy with it. So something has to raise the total back, and the only remaining channel is the energy dumped into the cold reservoir, $Q_C/T_C$. Requiring the total not to fall means $Q_C$ cannot be zero.

That is why power plants have cooling towers, why the exhaust of an engine is warm, and why "waste heat" is a structural requirement rather than an engineering failure. Efficiency improves when $T_H$ and $T_C$ are pushed further apart, and it reaches $100\%$ only in a limit nothing reaches.