# How can probability theory solve the most complicated problems of five unknowns?

#### Enjoyer

Greetings to All! How to solve such a difficult task? Perhaps there are complex theorems that only enlightened minds can understand?

Value: q; w; u; h; m; Is known
Value: A; B; C; D; E; Unknown
Value: X; The same

q = X * A

w = X * B

u = X * C

h = X * D

m = X * E

Need to find Value: X;

#### DarnItJimImAnEngineer

There is no unique solution. Easy way to tell is that you have six unknowns and only five equations.

Let's say q = heat transfer, w = work done, u = internal energy, h = enthalpy, m = mass of steam going through a power plant, where A, B, C, D, and E are the heat transfer rate, power, internal energy flux, enthalpy flux, and mass flux. X is then time. If you know q, and you know how much time X it took for that to occur, you can solve for the rate A, and then you can solve for B, C, D, and E, as well. Conversely, if you know A and q, you can calculate the amount of time X that was necessary. But every value of X is valid and will produce a different set of {A,B,C,D,E}. There is no unique solution if all six are unknown.

The best you can do is express things as ratios.
X = q/A,
A/B = q/w, etc.