Question

In the absence of compressed liquid tables, how is the specific volume of a compressed liquid at a given \(P\) and \(T\) determined?

Short answer

Answer: The incompressible substance model is a simplification used when precise data for a compressed liquid is unavailable. It assumes that the specific volume of the compressed liquid is constant and equal to the saturated liquid specific volume at the same temperature. To calculate the specific volume of a compressed liquid using this method, locate the saturated liquid specific volume (\(v_f\)) in the saturation table at the given temperature, and then assume that the specific volume of the compressed liquid (\(v\)) is equal to \(v_f\). This approach gives an approximation, which may not always be accurate for compressed liquids.

Step-by-step solution

Understand the incompressible substance model

The incompressible substance model is a simplification used when precise data for a compressed liquid is unavailable. In this model, the specific volume (\(v\)) is assumed to be constant and equal to that of the saturated liquid at the same temperature.

Locate the saturated liquid specific volume

Based on the given temperature (T), go to the saturation table (either water or refrigerant as required) and locate the row corresponding to the given temperature. Find the value of specific volume (\(v_f\)) for the saturated liquid state.

Calculate the specific volume of the compressed liquid using the incompressible substance model

Assuming that the specific volume of the compressed liquid is equal to the saturated liquid specific volume at the given temperature, you can use the following equation: Specific volume of compressed liquid (\(v\)) = Saturated liquid specific volume (\(v_f\)) v = v_f Now that you have determined the specific volume of the compressed liquid at the given pressure and temperature using the incompressible substance model, further calculations can be done as needed. Keep in mind that this is an approximation and may not always give accurate results for the specific volume of compressed liquids.