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Physics Question on thermal properties of matter

On a new scale of temperature (which is linear) and called the W scale, the freezing and boiling points of water are 39∘^{\circ}W and 239∘^{\circ}W respectively. What will be the temperature on the new scale, corresponding to a temperature of 39∘^{\circ}C on the Celsius scale?

A

78∘^{\circ}W

B

117∘^{\circ}W

C

200∘^{\circ}W

D

139∘^{\circ}W

Answer

117∘^{\circ}W

Explanation

Solution

In general, whenever we are to go from any known scale to any unknown scale, then we follow the equation (Temperature on known scale)−(LFP for known scale)(UFP−LFP)known\frac{(Temperature \: on\: known\: scale)-(LFP \:for \: known\: scale)}{(UFP - LFP)_{known}} = (Temperatureon unknown scale)−(LFP for unknown scale)(UFP−LFP)unknown\frac{(Temperatureon\: unknown \: scale)- (LFP\: for\: unknown\: scale)}{(UFP - LFP)_{unknown}} or 39−0100−0=t−39239−39\frac{39-0}{100-0}=\frac{t - 39}{239 - 39} or t=117∘Wt = 117^{\circ}W Note : LFP - Lower fixed point UFP - Upper fixed point