Question

The upper and lower fixed points of a thermometer are separated by \[180mm\]. What is the temperature in Celsius if the length of the mercury thread is \[90mm\] above the lower fixed point?

A) \[~90{}^\circ C\]
B) \[50{}^\circ C\]
C) \[45{}^\circ C\]
D) \[58{}^\circ C\]

Answer 1

Hint: Since it is a Celsius scale the upper fixed point and lower fixed point are determined based on the properties of water. The lower fixed point in Celsius scale is determined by the melting temperature of pure water. And it is given that LFP and UFP are separated by \[180mm\].We can use the equation which relates LFP, UFP and length of liquid thread at a temperature to find unknown temperature.
Formula used:
\[t=\dfrac{x-{{x}_{0}}}{{{x}_{100}}-{{x}_{0}}}\times 100\]

Complete answer:
We have,
\[t=\dfrac{x-{{x}_{0}}}{{{x}_{100}}-{{x}_{0}}}\times 100\] --------- 1
Where,
\[x-\text{ }length\text{ }of\text{ }liquid\text{ }thread\text{ }at\text{ }t\text{ }temperature\]
\[{{x}_{0}}~-length\text{ }of\text{ }liquid\text{ }thread\text{ }at\text{ }ice\text{ }point\]
\[{{x}_{100}}~-length\text{ }of\text{ }liquid\text{ }thread\text{ }at\text{ }steam\text{ }point\]
 \[t-unknown\text{ }temperature\]
Since it is a Celsius scale, the lower fixed point is \[0{}^\circ C\].
Then, \[{{x}_{0}}=0{}^\circ C\]
Given that upper fixed point and lower fixed point are separated by\[180mm\].
Then, \[{{x}_{100}}=180mm\]
Mercury thread is \[90mm\] above the lower fixed point. Hence, \[x=90mm\]
Now substitute the values of \[{{\text{x}}_{\text{0}}}\text{, x and }{{\text{x}}_{\text{100}}}\] in equation 1. We get,
\[Temperature, t=\dfrac{90}{180}\times 100=50{}^\circ C\]

So, the correct answer is “Option B”.

Additional Information:
To define a temperature scale in a thermometer, we need to choose two reference points, which are known as fixed points. In Celsius scale these fixed points are defined using properties of pure water. Those properties are; temperature of pure melting ice at normal atmospheric pressure and the temperature of pure boiling water at normal atmospheric pressure. The lower fixed point is determined by the temperature of pure melting ice and the upper fixed point is determined by temperature of pure boiling water. Once the Upper and lower points are fixed, we can now define a temperature scale.

Note:
There are many thermometers which use different temperature scales. These thermometers have different values of UFP and LFP. In the Celsius scale, upper and lower fixed points are usually separated by \[100\] divisions. Each division is a degree Celsius. It has LFP at \[0{}^\circ C\] and UFP at \[100{}^\circ C\]. In the Fahrenheit scale lower and upper fixed points are \[32{}^\circ F\] and \[212{}^\circ F\] respectively.