The Second Law

The second law of thermodynamics states that heat transfer occurs spontaneously only from higher to lower temperature bodies.

Irreversibility

The second law of thermodynamics deals with the direction taken by spontaneous processes. Many processes occur spontaneously in one direction only—that is, they areirreversible, under a given set of conditions. Although irreversibility is seen in day-to-day life—a broken glass does not resume its original state, for instance—complete irreversibility is a statistical statement that cannot be seen during the lifetime of the universe. More precisely, an irreversible process is one that depends on path. If the process can go in only one direction, then the reverse path differs fundamentally and the process cannot be reversible.

For example, heat involves the transfer of energy from higher to lower temperature. A cold object in contact with a hot one never gets colder, transferring heat to the hot object and making it hotter. Furthermore, mechanical energy, such as kinetic energy, can be completely converted to thermal energy by friction, but the reverse is impossible. A hot stationary object never spontaneously cools off and starts moving. Yet another example is the expansion of a puff of gas introduced into one corner of a vacuum chamber. The gas expands to fill the chamber, but it never regroups in the corner. The random motion of the gas molecules could take them all back to the corner, but this is never observed to happen.

One-Way Processed in Nature: Examples of one-way processes in nature. (a) Heat transfer occurs spontaneously from hot to cold and not from cold to hot. (b) The brakes of this car convert its kinetic energy to heat transfer to the environment. The reverse process is impossible. (c) The burst of gas let into this vacuum chamber quickly expands to uniformly fill every part of the chamber. The random motions of the gas molecules will never return them to the corner.

Second Law of Thermodynamics

The fact that certain processes never occur suggests that there is a law forbidding them to occur. The first law of thermodynamics would allow them to occur—none of those processes violate conservation of energy. The law that forbids these processes is called the second law of thermodynamics. We shall see that the second law can be stated in many ways that may seem different, but these many ways are, in fact, equivalent. Like all natural laws, the second law of thermodynamics gives insights into nature, and its several statements imply that it is broadly applicable, fundamentally affecting many apparently disparate processes. The already familiar direction of heat transfer from hot to cold is the basis of our first version of the second law of thermodynamics.

The Second Law of Thermodynamics(first expression): Heat transfer occurs spontaneously from higher- to lower-temperature bodies but never spontaneously in the reverse direction.

The law states that it is impossible for any process to have as its sole result heat transfer from a cooler to a hotter object. We will express the law in other terms later on, most importantly in terms of entropy.

Heat Engines

In thermodynamics, a heat engine is a system that performs the conversion of heat or thermal energy to mechanical work.

In thermodynamics, a heat engine is a system that performs the conversion of heat or thermal energy to mechanical work. Gasoline and diesel engines, jet engines, and steam turbines are all heat engines that do work by using part of the heat transfer from some source. Heat transfer from the hot object (or hot reservoir) is denoted as Q_h, while heat transfer into the cold object (or cold reservoir) is Q_c, and the work done by the engine is W. The temperatures of the hot and cold reservoirs are T_h and T_c, respectively.

Heat Transfer: (a) Heat transfer occurs spontaneously from a hot object to a cold one, consistent with the second law of thermodynamics. (b) A heat engine, represented here by a circle, uses part of the heat transfer to do work. The hot and cold objects are called the hot and cold reservoirs. Qh is the heat transfer out of the hot reservoir, W is the work output, and Qc is the heat transfer into the cold reservoir.

Because the hot reservoir is heated externally, which is energy intensive, it is important that the work is done as efficiently as possible. In fact, we would like W to equal Q_h, and for there to be no heat transfer to the environment (Q_c=0). Unfortunately, this is impossible. The second law of thermodynamics (second expression) also states, with regard to using heat transfer to do work: It is impossible in any system for heat transfer from a reservoir to completely convert to work in a cyclical process in which the system returns to its initial state.

A cyclical process brings a system, such as the gas in a cylinder, back to its original state at the end of every cycle. Most heat engines, such as reciprocating piston engines and rotating turbines, use cyclical processes. The second law, in its second form, clearly states that such engines cannot have perfect conversion of heat transfer into work done.

Efficiency

A cyclical process brings the system back to its original condition at the end of every cycle. By definition, such a system’s internal energy U is the same at the beginning and end of every cycle—that is, ΔU=0. The first law of thermodynamics states that ΔU=Q−W, where Q is the net heat transfer during the cycle (Q=Q_h−Q_c) and W is the net work done by the system. Since ΔU=0 for a complete cycle, we have W=Q. Thus the net work done by the system equals the net heat transfer into the system, or

[latex]\text{W} = \text{Q}_\text{h} - \text{Q}_\text{c}[/latex] (cyclical process),

just as shown schematically in (b).

Efficiency is one of the most important parameters for any heat engine. The problem is that in all processes, there is significant heat transfer Q_c lost to the environment. In the conversion of energy to work, we are always faced with the problem of getting less out than we put in. We define the efficiency of a heat engine (Eff) to be its net work output W divided by heat transfer to the engine Q_h:

[latex]\text{Eff} = \frac{\text{W}}{\text{Q}_\text{h}}[/latex].

Since W=Q_h−Q_c in a cyclical process, we can also express this as

[latex]\text{Eff} = \frac{\text{Q}_\text{h} - \text{Q}_\text{c}}{\text{Q}_\text{h}} = 1 - \frac{\text{Q}_\text{c}}{\text{Q}_\text{h}}[/latex] (for cyclical process),

making it clear that an efficiency of 1, or 100%, is possible only if there is no heat transfer to the environment (Qc=0).

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