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Solution of Equations Example Problem Desire to find the temperature (T) that corresponds to a desired pressure, P

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Method 1 You do the algebra to rearrange the equation: Then substitute for A, B, C, & P (without units!)

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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

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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

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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:

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Method 3 A := 7.02447 B := 1160.0 C := 224.0 P des := 760 Define the pressure function

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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.

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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)

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A := 7.02447 B := 1160.0 C := 224.0 P des := 760Tg := 76 Given T := find(T g ) T = 55.946 Solve block

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A := 7.02447 B := 1160.0 C := 224.0 Method 5 Plot the data and solve graphically.

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Method 4 Can have multiple unknowns in solve block: S1 := 1L S2 := 0.5L S3 := 1L S4 := 0.5 L Given

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Method 4 := Find(S2,S3,S4) = 0. 666446739 0. 841389008 0. 82472784 L

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Chapter 1 - Fundamentals 1.5 - Equations. Definitions Equation An equation is a statement that two mathematical statements are equal. Solutions The values.

Chapter 1 - Fundamentals 1.5 - Equations. Definitions Equation An equation is a statement that two mathematical statements are equal. Solutions The values.

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