"Triple fraction?"

"Triple fraction?"

Postby Guest » Fri May 10, 2019 1:31 pm

P1*V1/T1 = V2*P2/T2
How do we calculate in different way if one of these is unknown?
i.e. P2= P1*V1*T2/T1*V2
How about T2=?
What is the formula?
/ is the division
* is the multiplication

Re: "Triple fraction?"

Postby Guest » Wed May 15, 2019 11:32 am

[tex]]\frac{P_1V_1}{T_1}= \frac{P_2V_2}{T_2}[/tex]

To solve for any one unknown "undo" whatever is done to it,
[tex]P_2[/tex] has been multiplied by [tex]V_2[/tex] and divided by [tex]T_2[/tex]. To "undo" those divide both sides by [tex]V_2[/tex] and multiply by [tex]T_2[/tex]. And, of course, do that to both sides:
[tex]P_2= \left(\frac{P_1V_1}{T_1}\right)\frac{T_2}{V_2}= \frac{P_1V_1T_2}{T_1V_2}[/tex] as you have.

Solving for [tex]T_2[/tex] is just a little more complicated because [tex]T_2[/tex] is in the denominator. To undo that invert the fraction: [tex]\frac{1}{\frac{1}{x}}= x[/tex]. Inverting both sides [tex]\frac{T_2}{P_2V_2}= \frac{T_1}{P_1V_1}[/tex]. Now multiply both sides by [tex]P_2V_2[/tex]: [tex]T_2= \frac{T_1P_2V_2}{P_1V_1}[/tex].

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