Page 117 - Gas Adsorption Equilibria

2. Volumetry / Manometry 103

5.2 Outline of Theory and Calibration

If heat is generated inside the adsorption vessel of the SGC, Fig. 2.9, it
will be transferred via the sensor gas to the surrounding thermostat fluid.
According to the Newton-Fourier Law of heat transfer we have for the total
heat flow

Here K is an instrument parameter to be determined by calibration
experiments; T = T(t) indicates the time dependent average temperature of the
*
sensor gas and T = const is the temperature of the thermostat fluid
* )
surrounding the sensor gas jacket. For an ideal sensor gas the temperature T
easily can be related to its pressure as

In (2.42) are the (constant) volume and mass of the sensor gas and
its molar mass. Combining (2.41, 2.42) we get for the total heat released
during a process

As is the time dependent signal recorded by the pressure
difference manometer (P3, Fig. 2.9), with indicating the pressure in
the reference gas thermometer, the heat (Q) can be calculated from this
relation by simple integration. As an example pressure signals as
responses to Ohm’s heat inputs of (0.5, 1.0, 1.5...5.0) J inside the adsorption
vessel are presented in Figure 2.11.

* ) The Newton-Fourier Law (2.41) seems to be adequate for the heat transfer process from the
sensor gas to the thermostat as long as there is no turbulent convection within the gas, i. e.
for Grashof numbers [2.30, 2.31]. For situations with it has to be
generalized taking aftereffects, i. e. the history of the sensor gas temperature {T(s),
into account. This can be done by using the theory of Linear Passive Systems (LPS), cp.
Chap. 6 and the literature cited there. Details will be published in a forthcoming paper
[2.32].