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Question
The graph between two temperature scales A and B is shown in figure. Between upper fixed point and lower fixed point there are 150 equal division on scale A and 100 on scale B. The relationship for conversion between the two scales is given by ______.
Options
`(t_A - 180)/100 = t_B/150`
`(t_A - 30)/150 = t_B/100`
`(t_B - 180)/150 = t_A/100`
`(t_B - 40)/100 = t_A/180`
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Solution
The graph between two temperature scales A and B is shown in figure. Between upper fixed point and lower fixed point there are 150 equal division on scale A and 100 on scale B. The relationship for conversion between the two scales is given by `underline((t_A - 30)/150 = t_B/100)`.
Explanation:
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
Where LFP → Lower fixed point
UFP → Upper fixed point
From the graph, it is clear that the lowest point for scale A is 30° and the highest point for scale A is 180°.
The lowest point for scale B is 0° and the highest point for scale B is 100°. Hence, the relation between the two scales A and B is given by
`(T_A - (LFP)_A)/((UFP)_A - (LFP)_A) = (T_B - (LFP)_B)/((UFP)_B - (LFP)_B)`
⇒ `(T_A - 30)/(180 - 30) = (T_B - 0)/(100 - 0)`
⇒ `(t_A - 30)/150 = t_B/100`
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