# Laplace transform on thermodynamics equation

I'm trying to create a simple model of a single-flash geothermal plant which consist of 3 main parts (flash-separator, turbine, and condenser). Is there any way to create a transfer function using Laplace Transform (s-domain) of each parts based on the thermodynamics equation? • It depends on what you mean by "thermodynamics." Thermodynamics usually refers to equilibrium conditions. However, if the material- and energy balances are changing slowly enough and you are willing to include transport processes like heat transfer in the condenser into what you call thermodynamics, then the answer is yes. – Chet Miller Dec 3 '18 at 12:38
• given that I want to plot the turbine response and find the efficiency, from most of literature I read, they mainly use enthalpy and mass flow equation. The problem is I dont get how to transform the enthalpy and mass flow equation into a differential equation then use Laplace transform to find their transfer function in s-domain – dpw Dec 3 '18 at 12:41
• Normally, you are concerned with the steady-state operation of such systems, especially when doing process design. Is there a reason that you need to worry about the dynamic response (e.g., process control design)? – David White Dec 3 '18 at 18:20

## 1 Answer

The first thing you need to do is write down the time-dependent mass- and energy balance equations for the turbine (using the open system control volume version of the 1st law of thermodynamics). Then you express each the variables as the sum of a steady state part and a transient part. Then you solve for the steady state part. Then you linearize the time-dependent equations with respect to the perturbations about the steady state. Then you can use the Laplace transform for the linearized perturbations.