When equations are used in physics the most they can be is approximations. For very simple relationships the approximation is essentially perfect like F=ma. But when more complicated ideas are needed such as the structure of a star, a mathematical model that only approximates a star’s nature is constructed. This means that even if a physicist’s mathematics is correct their conclusion might be wrong simply because the equation they used didn’t really represent anything in reality.
For thermodynamics there are so many different permutations that often scientists will have to create their own models for unique systems. The equations will reveal an unknown variable or describe the balances between different chemicals present. But no matter how simple or how complicated all the models must pass a baseline test. The Gibbs-Duhem equation:
If a model does not fit this equation it is thermodynamically incorrect and certainly flawed. A paper has recently been published attempting to transform this equation into a set of universal physical principles. This would mean that instead of creating a model; putting through the equation; and finding it to be incorrect, a scientist could build the model up making sure all physical principles were correct during the process. This could lead to the universal thermodynamic model for solids, liquids and gases which still has yet to be found.