Question

The lengths of the mercury column of a mercury thermometer are 1.26cm and 20.86cm respectively at the standard fixed points. What is the temperature of body, which produces 9.0cm of this mercury column?

Answer 1

The temperature of the body is equal to 39.48°C

Why?

To find the temperature of the body that produces 9.0cm of this mercury column, we need to use the formula for linear interpolation. Also, the temperatures to use are based on the Celsius degrees scale.

For the fixed tempetatures, we have:

$1.26cm=0\°C(ColdWaterPoint)\\20.86cm=100\°C(BoilingWater)Point$

We need to use the following formula for linear interpolation:

$y=\frac{x-x_{1}}{x_{2}-x_{1}}*(y_{2}-y_{1})+y_{1}$

Then, we have:

$1.26cm=0\°C\\20.86cm=100\°C\\9.0cm=???\\\\x_{1}=1.26cm,y_{1}=0\°C\\\\x_{2}=20.86cm,y_{2}=100\°C\\\\x=9.0cm,y=???$

So, interpolating we have:

$y=\frac{(9cm-1.26cm)}{(20.86cm-1.26cm)}*(100\°C -0\°C)+0\°C\\\\y=0.39*100\°C=39.48100\°C$

Hence, the temperature of the body is equal to 39.48°C

Have a nice day!