TITLE.PM5

FIRST LAW OF THERMODYNAMICS 163

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/M-therm/Th4-4.pm5

Applying the energy equation to the system
h 1 = h 2
This shows that enthalpy remains constant during adiabatic throttling process.
The throttling process is commonly used for the following purposes :
(i) For determining the condition of steam (dryness fraction).
(ii) For controlling the speed of the turbine.
(iii) Used in refrigeration plant for reducing the pressure of the refrigerant before entry into
the evaporator.
Throttling process frequently encountered in practice was investigated by Joule and Thompson
(Lord Kelvin) in their famous porous plug experiment (Fig. 4.41). A stream of gas at pressure p 1
and temperature T 1 is forced continuously through a porous plug in a tube from which it emerges
at a lower pressure p 2 and temperature T 2. The whole apparatus is thermally insulated.
In this process (as earlier stated)
h 1 = h 2
Whether the temperature and internal energy change in a throttling process depends on
whether the fluid behaves as an ideal gas or not. Since the enthalpy of an ideal gas is a function of
temperature alone, it follows that
T 1 = T 2 for (throttling process)ideal gas ...(4.64)
and, therefore, u 1 = u 2
For an ideal gas, therefore, the throttling process takes place at
(i) constant enthalpy,
(ii) constant temperature, and
(iii) constant internal energy.
The enthalpy of a real gas is not a function of temperature alone. In this case
T 1 ≠ T 2 ...(4.65)
Also since the pv product may be different before and after throttling, the change in internal
energy is not zero, as it is in free expansion, but is given by
u 2 – u 1 = p 1 v 1 – p 2 v 2 ...(4.66)
Joule-Thompson and Joule Co-efficients
When a real gas undergoes a throttling process a change in temperature takes place. Let us
perform a series of the experiments on the same gas, keeping p 1 and T 1 constant, by varying the
pressure downstream of the plug to various values p 2 , p 3 , p 4 etc. After throttling let T 1 , T 2 , T 3 , T 4
etc. be the corresponding temperatures. Now if a graph is plotted between p and T (Fig. 4.42), a
smooth curve drawn through these points will be a curve of constant enthalpy because h 1 = h 2 = h 3
= h 4 etc.
It may be noted that this curve does not represent the process executed by the gas in
passing through the plug, since the process is irreversible and the gas does not pass through a
sequence of equilibrium states.
The slope of a constant enthalpy line or a p-T diagram at a particular state may be positive,
zero or negative value. The slope is called Joule-Thompson co-efficient, μ and is given by

μ =

∂

∂

T

p h

F

HG

I

KJ ...(4.67)

= 0 for ideal gas.