The temperature t on a thermometric scale is defined in terms of a property P by a relation $t = a e^{p} + b$
The values of P are found to be 1.56 and 8.25 at ice point and steam point the temperatures of which are assigned as 0 and 100 respectively. The temperature on this scale corresponding to value of P as 5.41 is

5.41

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5.84

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21.34

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52.33

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Solution

The correct option is B 5.84
For ice point, $0 = a e^{1.56} + b . . . (1)$
For ice point, $100 = a e^{8.23} + b . . . (2)$
For ice point, $t_{c} = a e^{5.41} + b . . . (3)$
Subtracting eq. (1) from (2), we get
$100 - 0 = a (e^{8.23} - e^{1.56}) . . . (4)$
Dividing eq. (4) by (5)
$\frac{100 - 0}{t_{c} - 100} = \frac{e^{8.23} - e^{1.56}}{e^{5.41} - e^{8.23}}$
$t_{o} = 5.84$

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