The third law of thermodynamics says reaching a temperature of absolute zero is impossible and makes it impossible for a Carnot cycle engine to achieve 100% efficiency.

Carnot Cycle

The French engineer, Sadi Carnot (1796 - 1832), did the pioneering analysis on the efficiency of heat engines. He found that the maximum possible efficiency for a heat engine occurred when it used a specific cycle, now called the Carnot cycle.

A heat engine is any engine that uses heat energy to do some form of useful work. A heat engine absorbs thermal energy, or heat, from a heat source known as the hot reservoir and rejects waste heat to what is known as the cold reservoir. For example a steam engine operating by using a fire to boil water, which moves a piston, has the heated steam as the hot reservoir and Earth's atmosphere, absorbing the waste heat, as the cold reservoir.

A Carnot cycle engine absorbs energy from the hot reservoir, at a high constant temperature. At a different part of the cycle, it releases energy to the cold reservoir, at a lower constant temperature. It does not change its temperature while either absorbing or releasing thermal energy. Physicists call this type of heat or energy transfer isothermal. The temperature changes occur when the engine is neither absorbing nor releasing thermal energy or any other form of energy. This Carnot cycle is an ideal cycle. Thermodynamic engineers strive for but do not achieve this ideal in real engines.

Efficiency and the Second Law of Thermodynamics

Carnot found that the efficiency of an engine operating on the Carnot cycle depends only on the temperatures of the hot and cold reservoirs. Carnot's formula gives the efficiency as 1 - Tc/Th. Tc and Th are the temperatures of the cold and hot reservoirs in the Kelvin temperature scale. If Tc is zero, then the efficiency is 1 or 100%.

The second law of thermodynamics states that the efficiency of any process must always be less than 100%. An alternate statement is that no heat engine can have an efficiency greater than the efficiency of an engine operating with the Carnot cycle.

The Carnot cycle allows 100% efficiency, if and only if the waste heat is dumped into a heat reservoir at a temperature of absolute zero. The third law of thermodynamics closes this loophole.

Absolute Zero

When an object's temperature decreases its internal heat energy causes the random motions of individual atoms and molecules to decrease. Random molecular motions are faster at higher temperatures and slower at lower temperatures.

The lowest possible temperature is when these random atomic and molecular motions are at the minimum possible energy. This temperature is absolute zero, which is the zero point in the Kelvin temperature scale. Absolute zero is -273.15 degrees Celsius or -459.67 degrees Fahrenheit.

Third Law of Thermodynamics

The third law of thermodynamics simply states that it is not possible to reach a temperature of absolute zero. It is possible to come arbitrarily close to absolute zero but not possible to reach that temperature by any process or series of processes.

If a temperature of absolute zero is impossible, then it is not possible for a Carnot cycle engine to reach 100% efficiency. The third law of thermodynamics closes the loophole that the Carnot cycle opens in the second law of thermodynamics.

Further Reading:

The Laws of Thermodynamics

The First Law Of Thermodynamics

Zemansky, M. and Dittman, H. Heat and Thermodynamics 7th ed., McGraw Hill, 1996.

Feynman, Leighton, & Sands, The Feynman Lectures on Physics vol. I, Addison Wesley, 1963.