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RF Cascade Workbook

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1996 -
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Kirt Blattenberger,

BSEE
- KB3UON

RF Cafe began life in 1996 as "RF Tools" in an AOL screen name web space totaling 2 MB. Its primary purpose was to provide me with ready access to commonly needed formulas and reference material while performing my work as an RF system and circuit design engineer. The Internet was still largely an unknown entity at the time and not much was available in the form of WYSIWYG ...

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Kirt's Cogitations™ #264

**These original Kirt's Cogitations™ may be reproduced (no more than
5, please) provided proper credit is given to me, Kirt Blattenberger.**

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Cog·i·ta·tion [koj-i-tey'-shun] – noun: Concerted thought or
reflection; meditation; contemplation.

Kirt [kert] – proper noun: RF Cafe webmaster.

Some of what you and I consider common knowledge is largely unrealized by most people. Call me a geek, but I take pleasure in pointing out to people that the Fahrenheit and Centigrade scales are equal at -40°, and I especially enjoy working out the simple proof for them. Most people appreciated the effort and are amazed, claiming to have never seen that before. When I read the following in

Since every once in a while people land on the RF Cafe website who do not have a background in science or engineering, I'll take this opportunity to present the aforementioned proof:

The conversions back and forth between Fahrenheit and Celsius are

1. F = (C * 1.8) + 32

2. C = (F - 32) / 1.8

As a quick test, almost everyone knows that 0°C = 32°F, so

C = (32 - 32) / 1.8 = 0 / 1.8 = 0

In the other direction,

F = (C * 1.8) + 32 = (0 * 1.8) + 32 = 0 + 32 = 32

Additionally, 100°C = 212°F, so

C = (212 - 32) / 1.8 = 180 / 1.8 = 100

Now for the proof. Substitute equation 1. into equation 2. to find where C = F,

C = (C * 1.8) + 32 = 1.8C + 32

Subtract 1.8C from both sides of the equation,

C - 1.8C = 32

-0.8C = 32

Divide both sides by -0.8,

C = 32 / (-0.8)

C = -40

So, C = F at -40

It works the same for substituting equation 2. into equation 1.,

F = (F - 32) / 1.8

Multiply both sides of the equation by 1.8,

1.8F = F - 32

1.8F - F = -32

0.8F = -32

F = -32 / 0.8

F = -40

So, F = C at -40

QED

The entire exercise takes less than a minute with pencil and paper. Enlighten a friend or relative the next time an opportunity arises.

Posted April 24, 2013