CHAP. 4: APPLICATION OF THERMODYNAMICS [CONTENTS] 112
4.2.1 Adiabatic process—Poisson’s equations
During an adiabatic process [see1.4.5], the system does not exchange heat with its surround-
ings, i.e.Q= 0. Work during an adiabatic process (both reversible and irreversible) is equal to
the change of internal energy
W= ∆U. (4.21)
Provided that the following conditions are fulfilled during an adiabatic process, i.e. that
- the process is reversible,
- the system exchanges only volume work with its surroundings,
- the system is an ideal gas,
- the heat capacitiesCV andCpdo not depend on temperature,
the following relations, calledPoisson’s equations, apply betweenT,pandV:
pVκ= const, p^1 /κV = const, (4.22)
T Vκ−^1 = const, V T^1 /(κ−1)= const, (4.23)
T p(1−κ)/κ= const, pTκ/(1−κ)= const, (4.24)where
κ=Cp
CV=
Cpm
CVm. (4.25)
Note:The curves defined by relations (4.22) through (4.24) are called reversible adiabatic
lines or isentropic lines.Example
An ideal gas expanded adiabatically from temperatureT 1 = 300 K and pressurep 1 = 1 MPa
to pressurep 2 = 100 kPa. Provided that Poisson’s equations hold and thatCpm =^52 R, find
temperatureT 2 after the expansion.