Mr. Rogers' AP Physics C: IB Physics Topics

Syllabus 1st Quarter 2nd Quarter 3rd Quarter 4th Quarter
IB SL Thermo IB HL Thermo IB HL Waves AP Review  

Topic 9: HL Thermal Physics (SL optional) - 2nd Law Of Thermodynamics

1st Law 2nd Law Processes Heat Engines HL Equations

The 2nd Law of Thermo is much harder to state let alone grasp, but is generally considered second only to the first law in terms of being immutable. Discovery of the 2nd Law of Thermo starting with a definition by Rudolf Clausius in 1850 pretty much put an end to the useless quest for a perpetual motion machine and opened the way for development of heat engines that actually work.

Definition - 2nd Law of Thermodynamics

Definition - Entropy

Definition #1: Kelvin–Planck formulation
It's impossible to construct a heat engine that, operating in a cycle, produces no effect other than the input of energy by heat from a reservoir and the performance of an equal amount of work. (p.670 Serway, 6th Edition, Physics for Scientists and Engineers)
Even if friction free, no heat engine operating in a cycle could convert 100% of its heat input into work output.

Perpetual Motion Machines: One ramification of the laws of thermo is that a perpetual motion machine cannot work in the real world. The 1st Law of Thermo says such a system would have a finite amount of mechanical energy which would slowly decline as it was converted to heat by friction. When the system reached zero mechanical energy it would stop. The 2nd Law delivers the final blow by saying that mechanical energy lost as heat could never be completely recovered and converted back into mechanical energy.


Definition #2: Clausius formulation
It is impossible to construct a cylindrical machine whose sole effect is to transfer energy continuously by heat from one object to another at higher temperature without the input of energy by work. (p.672 Serway, 6th Edition, Physics for Scientists and Engineers)
Heat does not flow from cold to hot objects unless a heat pump is used, and heat pumps require work input to operate.


Definition #3:The second law in terms of entropy

The entropy of the universe can be increased but not decreased. Likewise, the total entropy for an isolated system can be increased but not decreased.


The concept of entropy is inseparable from the 2nd Law of Thermodynamics and is frequently misunderstood. It takes time and effort to gain a useful working knowledge of the concept. The following is offered as a stating point.

Traditional Definition

A system property that is a measure of the degree of disorder of a thermodynamic system.

Here disorder can be understood as uncertainty about conditions on the microscopic level at an instant in time, for a particular macroscopic state.

Example: the temperature of a perfect gas. Here temperature is a macroscopic state representing the average kinetic energy of the the gas.

Assume that we start with a huge number of molecules all with the same speed, hence same kinetic energy—the uncertainty in speed on the microscopic level would be zero.  If the molecules were all moving in random directions, they would have random collisions at random angles resulting with a variety of speeds. Collisions between molecules would elastic so that  kinetic energy would be conserved, hence the average kinetic energy and temperature would be constant. Uncertainty over the speed of each individual molecule at an instant in time, however, would be much higher than the starting state and so the entropy would be higher.

 Alternative Definition

An indication of how much thermal energy is unavailable for doing work at a given temperature. Entropy times absolute temperature can be  interpreted as a measure of the unavailable thermal energy in a system.



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