2: Thermodynamics Review

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 1st 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.

whereis 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.

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