Solving Problems Using Ratios: Tips & Tricks

[Substance D]

Hello,

I'm currently in my 2nd year of physics and one thing I've noticed is how often problems can be solved using ratios, for example I had a problem in my thermodynamics class that involved finding a temperature after knowing its pressure and using the triple-point of water and its pressure as a reference point, I had put so much effort into this question and could not understand it, then a friend in my class solved in very easily using ratios. This is something that happens frequently with me (I think I over think the issue), anyways... does anyone have any tips in recognizing this type of problem solving using a ratio?

Thanks

 

[mgb_phys]

Look for closed systems.
Know general laws like the gas law.
Recognise opposing effects, eg. temperature and pressure.

Dimensional analysis is also a big help.

 

[Substance D]

I guess the problem I have with it is, if I have two equations, like with this example it was PV = nRT , but in this case I would have that equation twice (one for the totally known system and one for the "half" known system), and since n,R and V are constant I can just ignore them, but what is it that allows me to then say P1/T1 = P2/T2, which is what I did to solve for the unknown temp... does my question make sense, I hope it does

Thanks for the reply

 

[pixel01]

I am not sure if understood your question.
For this example, it is quite simple:
1st state : P1V1/T1 =nR and 2nd state: P2V2/T2 =nR so
P1V1/T1 = P2V2/T2
That equation holds for any fixed amount of gas (ideal)
So you can have some other derivative equations :
T = const ==> P1V1=P2V2
V=const ==> P1/T1=P2/T2 etc..

 

[Substance D]

oh, ok, yeah I get it now. thanks :)