RF Cascade Workbook

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Kirt
Blattenberger,

BSEE - KB3UON

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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