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Question: The fundamental interval, that is the number of divisions between lower fixed point (LFP) and upper ...

The fundamental interval, that is the number of divisions between lower fixed point (LFP) and upper fixed point (UFP) on the two scales X and Y are 50 and 150 respectively. The ice point on both the scales is0∘0{}^\circ . If the temperature on the X scale is15∘15{}^\circ , then what is the temperature on the Y scale.
A. 30∘30{}^\circ
B. 45∘45{}^\circ
C. 60∘60{}^\circ
D. 75∘75{}^\circ

Explanation

Solution

You could note down all the given values in the question as a first step. Then, you could think of the expression used for converting the given temperature in one temperature scale to another temperature scale. Then you could substitute the given values in that and hence get the answer accordingly.
Formula used:
Conversion between temperature scales,
X−LPF1UFP1−LFP1=Y−LFP2UFP2−LFP2\dfrac{X-LP{{F}_{1}}}{UF{{P}_{1}}-LF{{P}_{1}}}=\dfrac{Y-LF{{P}_{2}}}{UF{{P}_{2}}-LF{{P}_{2}}}

Complete answer:
In the question we are given the fundamental interval of two scales X and Y as 50 and 150 respectively. The ice point which is the lower fixed point is found to be the same on both scales as 0∘0{}^\circ . We are supposed to convert the given temperature of 15∘15{}^\circ on X scale in terms of Y scale.
We know that the fundamental interval is the number of divisions between the lower fixed point and upper fixed point. Let, LFP1LF{{P}_{1}} and UFP1UF{{P}_{1}} be the lower fixed point and upper fixed point of the X scale and LFP2LF{{P}_{2}} andUFP2UF{{P}_{2}} be that on the Y scale. Then, we know that the temperatures on two scales are related by,
X−LPF1UFP1−LFP1=Y−LFP2UFP2−LFP2\dfrac{X-LP{{F}_{1}}}{UF{{P}_{1}}-LF{{P}_{1}}}=\dfrac{Y-LF{{P}_{2}}}{UF{{P}_{2}}-LF{{P}_{2}}}
Now, we could substitute the given values,
15−050−0=Y−0150−0\dfrac{15-0}{50-0}=\dfrac{Y-0}{150-0}
⇒50Y=2250\Rightarrow 50Y=2250
∴Y=45\therefore Y=45
Therefore, we found that the Y scale will give a temperature of 45 when the X scale shows the temperature to be 15.

Hence, option B is found to be the answer.

Note:
Normally we choose that physical property that depends consistently and reproducibly on temperature to make a thermometer. Temperature is the measurement of how hot or cold a given substance is. The most common temperature scales are Celsius, Fahrenheit and Kelvin and Kelvin is the SI unit of temperature.