Untitled - Aerobib - Universidad Politécnica de Madrid

6 CHAPTER 1. THERMOCHEMISTRY
1.2 Thermodynamic functions of an ideal gas.
The equation of state
The state equation of an ideal gas is given by the expression
p
ρ = R gT, (1.7)
where
R g = R M g
(1.8)
is the particular constant of the gas, where R = 8.3144 joule/mol/grad = 1.9872 cal/mol/grad
is the universal constant of the gases.
Internal Energy
The internal energy of the gas is
∫ T
u = u 0 + c v (T ) dT. (1.9)
T 0
Here u 0 is the internal energy of the gas at temperature T 0 , c v is the specific heat at
constant volume, which depends on temperature as will be analyzed in §4, and T 0 is a
reference temperature. In particular, if c v is constant from T 0 to T , we have
u = u 0 + c v (T − T 0 ) , (1.10)
otherwise, in many applications c v is substituted by a mean value ¯c v . In such case
(1.9) takes the approximate form
u = u 0 + ¯c v (T − T 0 ) . (1.11)
Enthalpy
The gas enthalpy h is defined by
h = u + p ρ . (1.12)
Making use of the state equation (1.8) and of equation (1.9), one obtains for (1.12)
h = h 0 +
∫ T
T 0
c p (T ) dT, (1.13)