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Question
Calculate the temperature which has same numeral value on celsius and Fahrenheit scale.
Solution
To construct a scale of temperature, two fixed points are taken. First, the fixed point is the freezing point of water, it is called the lower fixed point. The second fixed point is the boiling point of water, it is called the upper fixed point. The temperature on one scale can be converted into other scales by using the following identity.
`("Reading on any scale - (LFP)")/((UFP) - (LFP))` = Constant for all scales
`(C - 0)/100 = (F - 32)/(212 - 32)`
Let T be the value of temperature having the same value on the Celsius and Fahrenheit scale, i.e. F = C = T
`(T - 32)/180 = T/100`
⇒ `T - 32 = 9/5`
⇒ `4/5 T = - 32`
⇒ T = – 40°C = – 40°F
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