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Suppose that a new temperature scale has been devised on which the melting point of some compound (−104.0°C) and the boiling point of the same compound (80.0°C) are taken as 0°S and 100°S, respectively, where S is the symbol for the new temperature scale. Derive an equation relating a reading on this scale to a reading on the Celsius scale. What would this thermometer read at 32.4°C?

Question

Suppose that a new temperature scale has been devised on which the melting point of some compound (−104.0°C) and the boiling point of the same compound (80.0°C) are taken as 0°S and 100°S, respectively, where S is the symbol for the new temperature scale. Derive an equation relating a reading on this scale to a reading on the Celsius scale. What would this thermometer read at 32.4°C?

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Step 1

Consider the equation S = aC+b here, S denotes new temperatu...

The -104°C is taken as 0°S, then
S aCb
0 a(-104)b
b 104 a
The 80°C is taken as 100°S, then
S aCb
100 a (80) b
100 a (80) 104 a
100 184 a
a 1.84
b 104 a
b 104 x1.84
b 191.36
Required equation is S (1.84)C
191.36
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The -104°C is taken as 0°S, then S aCb 0 a(-104)b b 104 a The 80°C is taken as 100°S, then S aCb 100 a (80) b 100 a (80) 104 a 100 184 a a 1.84 b 104 a b 104 x1.84 b 191.36 Required equation is S (1.84)C 191.36

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