Presentation on theme: "Solution of Equations Example Problem Desire to find the temperature (T) that corresponds to a desired pressure, P."— Presentation transcript:
Solution of Equations Example Problem Desire to find the temperature (T) that corresponds to a desired pressure, P
Method 1 You do the algebra to rearrange the equation: Then substitute for A, B, C, & P (without units!)
Method 2 Let Mathcad do the algebra for you Put the “T” in the blue edit box, click Symbolic / Variable / Solve Copy / paste the solution to a variable
Method 3 Solve the problem “approximately” using the “root” function in Mathcad This function takes an initial guess at the solution and numerically finds a root. Good for finding a single root of a non-linear function
Method 3 A := 7.02447 B := 1160.0 C := 224.0 Desire T where P = 760 mm Hg For acetone, with P in mm Hg and T in C, A, B, C are:
Method 3 A := 7.02447 B := 1160.0 C := 224.0 P des := 760 Define the pressure function
Guessestimate a TTg := 76 Method 3 Use the root function T := root(P des -P(T g ),T g ))T = 55.946 Root drives the first argument to zero by adjusting the second argument.
Method 4 “Solve” block or Given / find block Note: Given & Find are keywords in Mathcad! Define all variables, including guesses for the unknowns Start with “Given” keyword Type equations using = (ctrl =) sign. Close with find (list of unknowns)
A := 7.02447 B := 1160.0 C := 224.0 P des := 760Tg := 76 Given T := find(T g ) T = 55.946 Solve block
A := 7.02447 B := 1160.0 C := 224.0 Method 5 Plot the data and solve graphically.
Method 4 Can have multiple unknowns in solve block: S1 := 1L S2 := 0.5L S3 := 1L S4 := 0.5 L Given