Expert: Daniel Mazur - 9/9/2009

Question
Hi Daniel,

In an isothermal process, say a process on an ideal gas in a a container fitted with a light, frictionless piston, the entire heat that is supplied to the system, is converted into mechanical work.

Isn't this a violation of the second law of thermodynamics which states that heat supplied to a system cannot be completely converted into mechanical work....??

Aren't the isothermal processes just an idealisation then???

Thanks,
Shikhin

Answer
Dear Shikhin,

that version of the Second Law of thermodynamics speaks about efficiency of cycles (engines, motors), not about partial processes. Perpetuum mobile, whose realization is delared impossible by the Second Law, is in its nature an engine, a cyclic process.
X: Heat supplied to a system cannot be completely converted into mechanical work IN A CONTINUOUS, CYCLIC PROCESS.
The Carnot cycle consists of 2 isotherms and 2 adiabatic processes and its efficiency is thus defined as (T_hi - T_lo)/T_hi. You cannot define this ratio for a single isotherm.

All the "elementary processes" are an idealization at some level. We can, for example, measure and control the temperature only to a certain degree of precision. The real-life isotherms really meet with the theoretical isotherms only, when the process is really, really slow. So much so that they are impractical for real engines. You must distinguish, when you speak about the real-life processes and when about their theoretical counterparts. Still, this has nothing to do with efficiency, which is only defined for cycles.

Take care,
Daniel