# The steam point and the ice point of a mercury thermometer are marked at 80° and 20°. What will be the temperature in centigrade mercury scale when this thermometer reads 32°?

20° C

Explanation:

Given,

Steam point of the given scale, Tsteam, is 80°,

Ice point of the given scale, Tsteam, is 20°,

Temperature in centigrade scale corresponding to 32° , t=?

Formula used

The temperature of a mercury thermometer can be assumed to be in linear relation with its mercuric height or length. So the Temperature ( can be represented as

,

where represents the length; are constants depending on the steam (80°) and ice point (20°) of this scale

The centigrade mercury scale temperature ( can be represented as,

,

Where represents the length, and are constants depending on the steam (100°) and ice point (0°) of this scale.

We can conclude that, for fixed steam and ice points, the temperature is directly proportional to the mercuric height.

As both the scales use the mercuric height as the measuring parameter, these scales can be compared as;

Where represents the temperatures in the given mercury scale and represents that of the Centigrade scale.

By putting the given values in the above equations;

So,

Hence, temperature in centigrade scale corresponding to 32° of the given scale is 20°C (Ans.)

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