# Heat Transfer and the Second Law of Thermodynamics

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

Two thermal reservoirs at the same temperature, , can, in concept, exchange an increment of heat in either direction. Since it can just as easily flow in the opposite direction, this represents what is known as a reversible process and can be designated . By convention, is positive if heat flows into a reservoir and negative () if it flows out. When , it is a matter of experience that flows spontaneously (or irreversibly) from the hotter to the cooler reservoir. One can still set if one conceptualized an infinite number of intermediate reservoirs at temperature increments varying infinitesimally between and .

[more]
Contributed by: S. M. Blinder (April 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

A differential statement of the first law of thermodynamics can be written , where , , and represent heat, work, and energy, respectively. Applied to a reversible process in an ideal gas, this can be specialized to , where is the heat capacity at constant volume (equal to per mole for a monatomic ideal gas). Using the ideal gas law for 1 mole, , we can write , which is not an exact differential—showing that is not a function of state. Clearly, however, is an integrating factor for this expression, giving . This introduces a new function of state with , where is called the entropy. This turns out to be a general result applicable to all thermodynamic systems.

See any textbook on physical chemistry and many on general chemistry.

## Permanent Citation