# Math question: why do they do this step in transforming a formula? (in calculating absolute zero)

**URL:** <https://boards.straightdope.com/t/math-question-why-do-they-do-this-step-in-transforming-a-formula-in-calculating-absolute-zero/991613>\
**Category:** Factual Questions\
**Created:** [October 15, 2023, 8:50pm UTC](https://boards.straightdope.com/t/math-question-why-do-they-do-this-step-in-transforming-a-formula-in-calculating-absolute-zero/991613 "2023-10-15T20:50:33Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![dstarfire](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dstarfire/32/5762_2.png) [@dstarfire](https://boards.straightdope.com/u/dstarfire)\
**Post date:** [October 15, 2023, 8:50pm UTC](https://boards.straightdope.com/t/math-question-why-do-they-do-this-step-in-transforming-a-formula-in-calculating-absolute-zero/991613/1 "2023-10-15T20:50:33Z")

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from this video (at timestamp 7:36): [https://youtu.be/wR2tOLShFmY?si=PRfQue1CqV5AG8fE&t=456](https://youtu.be/wR2tOLShFmY?si=PRfQue1CqV5AG8fE&t=456) about calculating the value of absolute zero by measuring the volume of a gas at 2 different temperatures.  
We’re coming up with a single formula that takes in the temperatures and volumes at the two different points (T1/T2 and V1/V2, respectively)

Our base formula is  
V/a = x+T (I’ll explain a at the end, it’s a constant that is the same at both measurements)  
Then, for our specific measurements, the formulas are:  
V1/a=X+T1  
V2/a=x+T2

Then, we multiply both sides of the second formula by (V1/V2). **Why?** What is the principle or logic for picking that operator? Sure, it’s a valid operation (generally you can do whatever you want to an equation as long as you do it to both sides), I just don’t get the logical leap there.

trivia:‘a’ in this formula represents the ‘nR/P’ portion of the ideal gas law.

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**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\
**Post date:** [October 15, 2023, 9:02pm UTC](https://boards.straightdope.com/t/math-question-why-do-they-do-this-step-in-transforming-a-formula-in-calculating-absolute-zero/991613/2 "2023-10-15T21:02:42Z")

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> [@dstarfire](#):
>
> Then, we multiply both sides of the second formula by (V1/V2). **Why?**

To turn the left side into V1/a, matching the left side of the first equation. You then get two expressions that are both equal to V1/a, so you can set them equal to each other (or equivalently, set their difference equal to 0, which is how the video does it).

Multiplying by V1/V2 is equivalent to dividing by V2 and multiplying by V1.

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**Author:** ![dstarfire](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dstarfire/32/5762_2.png) [@dstarfire](https://boards.straightdope.com/u/dstarfire)\
**Post date:** [October 15, 2023, 9:10pm UTC](https://boards.straightdope.com/t/math-question-why-do-they-do-this-step-in-transforming-a-formula-in-calculating-absolute-zero/991613/3 "2023-10-15T21:10:17Z")

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ah-HA!! Yes!! Now it makes sense.

Thank you very much.