Day 99

As noted in the previous lesson, not all the heat supplied to a heat engine can be converted to mechanical work. This is true for all types of heat engines and is the basis for a second law of thermodynamics, which was first formulated by German physicist Rudolf Clausius, and later restated as the Kelvin-Planck statement.

2nd Law of Thermodynamics

It is impossible to construct a heat engine that, operating in a cycle, produces no other effect than the absorption of energy from a reservoir and the performance of an equal amount of work.

(NOTE: A heat engine is a device that converts internal energy to other useful forms of energy, mainly electrical and mechanical energies.) A schematic drawing of a heat engine (above) shows that the engine receives energy (Qh) from a hot reservoir and expels energy (QL) to a cold reservoir, doing work between.

It is possible to operate a heat engine in reverse. Energy is sent in, resulting in energy being extracted from the cold reservoir and transferred to the hot reservoir. Such devices are called heat pumps (i.e., refrigerators, freezers, air conditioners).

The thermal efficiency of a heat engine is defined as the ratio of the work done by the engine to the energy absorbed at the higher temperature during one cycle.

Basically, the thermal efficiency of a heat engine is the ratio of what you gain (work) to what you give (energy transfer at the higher temperature).

There is no perfectly efficient heat engine (see 2nd law of thermodynamics).

However, a French engineer, Sadi Carnot, described a theoretical engine (Carnot engine) and showed that a heat engine operating in an ideal, reversible cycle between 2 energy reservoirs is the most efficient engine possible.

Carnots Theorem

No real engine operating between two energy reservoirs can be more efficient than a Carnot engine operating between the same two reservoirs.

Carnot showed that the thermal efficiency of a Carnot engine is

Ec = 1 – [Tc/Th]

In general, the change in internal energy of any system is Q = m X Δ T X C

Q = change in internal energy; m = mass; ΔT = change in temperature; C = specific heat of substance)

NOTE: Specific heat = heat capacity of a material per unit mass for solids and liquids
However, this value is not fixed for gases. The value of the specific heat for gases varies for constant pressure and constant volume. When the pressure is held constant, added energy must be provided to do the work required to produce the volume increase. This added work equals the pressure times the change in volume. Therefore, C (constant pressure) is greater than C (constant volume). (Although this is true for solids and liquids, the amount of change is so small as to be negligible.)

While the zeroth law of thermodynamics involves the concept of temperature and the first law of thermodynamics involves the concept of internal energy, the second law of thermodynamics involves the concept of entropy S. Entropy is the internal energy of a system that cannot be converted into work. The difference in entropy is important here. If an amount of heat Q is added to a system that is at a Kelvin temperature T, the change in entropy S (J/K) is ΔS =ΔQ/T. If heat is removed from a system Q is negative and the change in S is also negative.
This leads to a restating of the second law of thermodynamics:

A natural process always takes place in such a direction as to increase the entropy in the universe. In the case of an isolated system, it is the entropy of the system that tends to increase. All natural processes are irreversible and involve increase in entropy.

Answer the following question:

Which of the following is true for the entropy change of a system that undergoes a reversible, adiabatic process?
a. ∆ S <  0
b. ∆ S =  0
c. ∆ S >  0