The specific heat at constant pressure (cP) or constant volume (cV) is the heat capacity per unit mass (m):
The difference of the thermal heat capacities (or specific heats) in an ideal gas is the gas constant (Rgas = 8.31 J Mole-1 K-1):
where NA is Avogadro's number, the number of particles in one mole (= 6.022 X1023 particles), and k is Boltzmann's constant.
Assume we have an atmosphere composed of an ideal gas which is convecting. A parcel of this air moves adiabatically (dQ = 0). Equation (6.10) then becomes dU = — PdV. (6.16)
Using the relationships in Eqs. (6.11) and (6.14), we find that cy dT = —PdV
The ratio of the specific heats, or thermal heat capacities, occurs often in thermo-dynamic applications and is indicated by the parameter y:
The adiabatic lapse rate of a dry atmosphere is obtained by combining the thermodynamic equation, equation of hydrostatic equilibrium, and ratio of the specific heats:
This is often rewritten as
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