Process temperatures

Many fundamental relationships in thermodynamics feature temperature as a central variable. It determines density, pressure, reaction rate, heat flux and state of matter.

A simple example is the ideal gas law:

p ⋅V = n ⋅ R ⋅ T

Here, p is the pressure, V the volume, n the amount of substance, R the universal gas constant and T the absolute temperature. The equation shows that pressure, volume and temperature are directly linked.

For heat transfer processes, the temperature difference is the driving force:

Q˙ = U·A·(T₁-T₂)

Here, Q˙​ is the heat flux, U is the overall heat transfer coefficient, A is the heat transfer area, and T₁​ and T₂​ are the temperatures of the systems involved.

Chemical and physical transformations are also highly temperature-dependent. The reaction rate can often be described using the Arrhenius equation:

K = A · exp(- E_A/(R · T))

Here, k is the reaction rate constant, A is a pre-exponential factor, E_A is the activation energy, R is the gas constant and T is the absolute temperature. Even small changes in temperature can have a significant impact here. The process temperature plays a central role in phase transitions. For evaporation, the following applies:

Q˙​= m˙ · Δh_v

Here, m˙ is the mass flow rate of the evaporating substance and Δh_v ​is the specific enthalpy of evaporation. The heat transfer takes place at the phase boundary and is temperature-dependent.

In addition to the absolute value of the process temperature, its accuracy and dynamics are crucial. Inaccurate temperature measurement can lead to incorrect process decisions. A measurement that is too slow can destabilise or delay control loops.