__Second Law
of Thermodynamics__

** **

For
any process in a closed system,

_{}

where
dQ is the heat transferred at temperature T to the system, and ds is the
resulting increase in entropy of the system.

For
a control volume, the entropy inequality may be written as

_{}

For
a change in an isolated system (no energy or mass transfer),

_{}

__Reversible
Process__

_{}

Rearranging
terms,

_{}

_{}from the 1^{st}
Law of Thermodynamics.

If
the only work being that is that due to volume change against pressure,

_{}

Applicable
to a closed system in internal equilibrium with the only work being that due to
volume change against a pressure.

__Equations
of State__

For
a system composed of a pure substance at equilibrium, only two independent
static properties need be specified to describe the thermodynamic state of the
system. The relation between any two properties of such a system is called an
equation of state.

__Thermal Equation of State__

For
a thermally perfect gas,

_{}

where
p is absolute pressure, r is density, T is absolute temperature, and R is the gas constant for
the particular gas.

_{}where_{}is the
"universal gas constant", a constant for all gases, and _{}is the molecular
weight of the gas. _{}has the value of 8314
Joules per Kelvin per kilogram-mole.

*Note: At
extremely high temperatures, such as those encountered in flames, and in hypersonic flight (>
2500K) nitrogen and oxygen start dissociating into single atoms, so that the
effective molecular weight of air decreases.
*