TITLE.PM5

164 ENGINEERING THERMODYNAMICS

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/M-therm/Th4-4.pm5

If we carry out other series of experiments similar to described above starting from different
initial states, we can obtain a family of constant enthalpy curves as shown in Fig. 4.43. The states
where μ = 0 are called ‘inversion states’ and locus of these states is called the inversion curve.

Fig. 4.43. Inversion curve.
The region inside the inversion curve is the cooling region since μ is positive, and tempera-
ture falls with fall in pressure.
The region outside the inversion curve is the heating region since μ is negative and tem-
perature rises with fall in pressure.
Cooling can take place only if the initial temperature before throttling is below the maxi-
mum inversion temperature. This temperature is about 5Tc.
The maximum inversion temperatures of some gases are given below :
(i) He = 24 K (ii) H 2 = 195 K
(iii) Air = 603 K (iv) N 2 = 261 K
(v) A = 732 K (vi)CO 2 = 1500 K.
The free expansion process is also a Joule (not Joule-Thompson). The Joule co-efficient is
defined by

Joule co-efficient = η = – ∂

∂

F

HG

I

KJ

T
v u
...(4.68)
For free expansion of gases the experimental data obtained is limited. From the data avail-
able it appears that η is positive (i.e., cooling accompanies a fall in pressure or increase in specific
volume).
Note. The throttling process is used in the liquification of gases where μ is positive.
STEADY FLOW SYSTEMS
Example 4.35. 10 kg of fluid per minute goes through a reversible steady flow process. The
properties of fluid at the inlet are : p 1 = 1.5 bar, ρ 1 = 26 kg/m^3 , C 1 = 110 m/s and u 1 = 910 kJ/kg and
at the exit are p 2 = 5.5 bar, ρ 2 = 5.5 kg/m^3 , C 2 = 190 m/s and u 2 = 710 kJ/kg. During the passage,
the fluid rejects 55 kJ/s and rises through 55 metres. Determine :
(i)The change in enthalpy (∆ h) ;
(ii)Work done during the process (W).