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Second Law Of Thermodynamics | Formulas, Equations, Examples

The second law of thermodynamics has several forms of expression. One of them states that no heat engine is capable of completely converting all the energy it absorbs into usable work (Kelvin-Planck formulation). Another way of stating it is to say that the real processes occur in such a sense that the quality of the energy is lower because the entropy< at i=5> tends to increase.

Second law of thermodynamics

This law, also known as the second principle of thermodynamics, has been expressed in different ways over time, from the beginning of the 19th century to the present, although its origins date back to the creation of the first steam engines in England. , at the beginning of the 18th century.

But although it is expressed in many ways, in all of them there underlies the idea that matter tends to get disordered and that no process is efficient 100%, since losses will always exist.

All thermodynamic systems adhere to this principle, starting with the universe itself to the morning cup of coffee waiting calmly on the table exchanging heat with the environment.

Coffee cools as time passes, until it is in thermal equilibrium with the environment, so it would be very surprising if one day the opposite happened and the environment cooled down while the coffee heated up by itself. It is unlikely to happen, some will say impossible, but it is enough to imagine it to have an idea of ​​the sense in which things happen spontaneously.

In another example, if we slide a book across the surface of a table, it will eventually stop, because its kinetic energy will be lost as heat due to friction.

The first and second laws of thermodynamics were established around 1850, thanks to scientists of the stature of Lord Kelvin –creator of the term “thermodynamics”-, William Rankine –author of the first formal text on thermodynamics- and Rudolph Clausius.

Formulas and equations OF Second Law of Thermodynamics

Entropy -mentioned at the beginning- helps us establish the sense in which things occur. Let’s go back to the example of bodies in thermal contact.

formula of second law of thermodynamics

When two objects at different temperatures come into contact and finally after some time reach thermal equilibrium, they are driven to do so by the fact that the entropy reaches its maximum, when the temperature of both is the same.

Denoting entropy as S, the change in entropy ΔS< a i=4> of a system is given by:

the change in entropy ΔS

Q is heat in joules and T is temperature in kelvins. In the International System of SI units, entropy is given in joules/kelvins or J/K.

The change in entropy ΔS indicates the degree of disorder in a system, but there is a restriction in the use of this equation: it is Applicable only to reversible processes, that is, those in which the system can return to its original state without leaving a trace of what happened.

In irreversible processes, the second law of thermodynamics manifests itself as follows:

Reversible and irreversible processes

The cup of coffee always cools and is a good example of an irreversible process, since it always occurs in only one direction. If you add cream to the coffee and stir, you will get a very pleasant combination, but no matter how much you stir again, you will not have the coffee and the cream separate again, because stirring is irreversible.

Although most everyday processes are irreversible, some are almost reversible. Reversibility is an idealization. For it to be carried out, the system must change very slowly, in such a way that at each point it is always in equilibrium. In this way it is possible to return it to a previous state without leaving a mark on the surroundings.

Processes that come close to this ideal are more efficient, since they deliver a greater amount of work with less energy consumption.

The force of friction is responsible for much of the irreversibility, because the heat generated by it is not the type of energy that is sought. In the book sliding across the table, heat from friction is energy that is not recovered.

Even if the book returns to its original position, the table will have remained hot as a trace of the coming and going on it.

Now look at an incandescent light bulb: most of the work done by the current passing through the filament is wasted on heat due to the Joule effect. Only a small percentage is used to emit light. In both processes (book and light bulb), the entropy of the system has increased.

Applications Of 2ND Law Of Thermodynamics

An ideal motor is one that is built using reversible processes and lacks friction that causes energy waste, converting almost all the energy thermal in usable work.

We emphasize the word almost, because not even the ideal engine, which is Carnot’s, has 100% efficiency. The second law of thermodynamics ensures that this is not the case.

Carnot engine

The Carnot engine is the most efficient engine that can be devised. It operates between two temperature reservoirs in two isothermal processes – at a constant temperature – and two adiabatic processes – without thermal energy transfer.

Carnot Engine Diagram

The graphs called PVpressure diagrams – volume– clarify the situation at a glance:

On the left, in figure 3 is the diagram of the Carnot engine C, which takes heat Q1 from the tank that is at temperature T1, converts that heat into work W and gives up the waste Q2 to the coldest tank, which is at temperature T2.

Starting from A, the system expands until it reaches B, absorbing heat at the fixed temperature T1. At B, the system begins an adiabatic expansion in which no heat is gained or lost, to reach C.

At C another isothermal process begins: that of transferring heat to the other colder thermal reservoir that is at T2. As this happens, the system is compressed and reaches point D. There a second adiabatic process begins to return to the starting point A. In this way a cycle is completed.

The efficiency of the Carnot engine depends on the kelvin temperatures of the two thermal tanks:

Maximum efficiency = (Qinput – Qoutput ) /Qinput = 1 – (T2 /T1)

Carnot’s theorem states that this is the most efficient heat engine available, but don’t rush to buy it. Remember what we said about the reversibility of processes? They have to happen very, very slowly, so the power output of this machine is practically zero.

Second Law Of Thermodynamics Examples

Second Law Of Thermodynamics examples in real life

The second law of thermodynamics is implicit in all processes that occur in the Universe. Entropy is always increasing, although in some systems it appears to be decreasing. For this to happen, it must have increased elsewhere, so that the overall balance is positive.

  1. In learning there is entropy. There are people who learn things well and quickly, in addition to being able to remember them easily later. It is said that they are people with low-entropy learning, but they are surely less numerous than those with high entropy: those who have a harder time remembering the things they study.

–2. A company with disorganized workers has more entropy than one in which workers carry out tasks in an orderly manner. It is clear that the latter will be more efficient than the former.

– 3. Friction forces generate less efficiency in the operation of machinery, because they increase the amount of energy dissipated that cannot be used efficiently.

– 4. Rolling a die has a higher entropy than flipping a coin. After all, flipping a coin only has 2 possible outcomes, while rolling a die has 6. The more events that are probable, the more entropy there is.

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