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Mathematical Formulae

Rearranging Equations III

The formulae we have met so far have been fairly straight forward in that one variable is the subject of the formula and we have been asked to make the other variable the subject of the formula.  Sometimes you may be faced with problems which have more variables, or the expression you are given is subject to operations as well.  These can be dealt to in much the same way as before, treating the other variables as a constant term.

Example

Make i the subject of the mirror equation:

1/0 +1/i = 1/f

Operations required for calculating the LHS from i:

Take i raise to the power -1 the add 1/o to get 1/f

Reversing the above (Click on the question marks to view the inverse operations):

 

 
 
Starting with 1/f subtract 1/o, simplify, then raise to the power -1 to get i

Example

Make T the subject of the ideal gas equation: pV = nRT

 

T
*nR
right arrow
nRT = pV
T = PV/RT
/nR
left arrow
pV

The real gas equation must take into account the effect of attractions and repulsions between particles. Make T the subject of the formula.

(p + an2/V2)(V - nb)= nRT

T
*nR
right arrow
nRT = (p+ an2/V2)(V - nb)
T = (p+ an2/V2)(V - nb)/(nR)
/nR
left arrow
(p+ an2/V2)(V - nb)

Exercise

Make p the subject of the real gas formula.   

P=(nRT)/(V-nb) - a*n^2*V^2

More Examples

 

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