General Equation Question about division

I have a physics problem that the solution requires the division of one equation by another equation. It is just a question about the ideal gas law and finding final pressure as temperature and volume change.

My question is in what general cases does an algebra problem require the division operation? Or, more generally, what typical question or phrase might I look for to tell me that I should consider using some operation to combine equations?

A link would be sufficient, I just haven't found anything to answer my questions.

Thanks for information.

Re: General Equation Question about division

Quote:

Originally Posted by

**Bowlbase** My question is in what general cases does an algebra problem require the division operation? Or, more generally, what typical question or phrase might I look for to tell me that I should consider using some operation to combine equations?

Elaborate please.

Re: General Equation Question about division

For instance, this Phys problem was: a tire is inflated at a temperature of 10c at normal atmospheric pressure. During the process, the air is compressed to 28% of its original volume and temperature is increased to 40c. What is the tire pressure?

Ideal gas law: PV=nRT

The solution being the final gas law equation divided by the initial. I just don't know how to jump to this conclusion to divide the two. Why divide and not multiply/add/subtract? I can do the math but can't find the path to the solution. Is it because its the only operation that makes physical sense or is there some other reason that I don't understand. I just never would have thought to do this without the solution manual.

Re: General Equation Question about division

Its basically something like this. Leave the ideal gas equation for ones

x=a*b

now consider two sets of data

(x1,a1,b1) and (x2,a2,b2)

you know x1,a1,b1,a2,b2 and need to find x2.

so how would you do it ?

Its not about division and all....you dont have to think that way. Its about find x2.

Same goes for that equation

p1v1=n1rT1

and

p2v2=n2rT2

plug the value and find the unknown

Re: General Equation Question about division

My question is why division to find 'x2' in this case? should I just be asking myself which operation would remove as many variables as possible while leaving the one I want? If so I can understand that. I just want to make sure I'm not missing something basic.

Re: General Equation Question about division

Bang on!

When you get around trying it, you find dividing is the most efficient way.

Re: General Equation Question about division

Hi bowlbase,

The equation you should be using is p1,v1/T1 = p2,v2/T2 T = deg K 273 + deg C

p1 = 1atm v2 =.28 v1 Plug in and calculate the tire pressure in atm

Re: General Equation Question about division

Personally, I would favor learning what the formula **means** rather than memorizing tricks that can be use mindlessly.