Parameterized models of biophysical and mechanical cell properties are important for predictive mathematical modeling of cellular processes. The concepts of turgor, cell wall elasticity, osmotically active volume, and intracellular osmolarity have been investigated for decades, but a consistent rigorous parameterization of these concepts is lacking. Here, we subjected several data sets of minimum volume measurements in yeast obtained after hyper-osmotic shock to a thermodynamic modeling framework. We estimated parameters for several relevant biophysical cell properties and tested alternative hypotheses about these concepts using a model discrimination approach. In accordance with previous reports, we estimated an average initial turgor of 0.6 ± 0.2 MPa and found that turgor becomes negligible at a relative volume of 93.3 ± 6.3% corresponding to an osmotic shock of 0.4 ± 0.2 Osm/l. At high stress levels (4 Osm/l), plasmolysis may occur. We found that the volumetric elastic modulus, a measure of cell wall elasticity, is 14.3 ± 10.4 MPa. Our model discrimination analysis suggests that other thermodynamic quantities affecting the intracellular water potential, for example the matrix potential, can be neglected under physiological conditions. The parameterized turgor models showed that activation of the osmosensing high osmolarity glycerol (HOG) signaling pathway correlates with turgor loss in a 1:1 relationship. This finding suggests that mechanical properties of the membrane trigger HOG pathway activation, which can be represented and quantitatively modeled by turgor.