Question

The lower and upper fixed points of a mercury in glass thermometer are marked X and 180mm respectively. on a particular day, the mercury meniscus in the thermometer rises to 60mm. if the corresponding reading n a celcius scale is 20 degree celcius, what is the value of X.

Answer 1

To find the value of X using the information given, we can use the linear relationship that exists in a thermometer, where the level of mercury corresponds to a specific temperature.

Let's set up the scenario based on the information provided:

1. The lower fixed point (X) corresponds to 0°C.
2. The upper fixed point (180 mm) corresponds to 100°C.
3. At 20°C, the mercury rises to 60 mm.

We can use the two fixed points to derive a linear equation for the temperature in terms of the height of the mercury column. The relationship can be expressed as follows:

\[
\text{Temperature (°C)} = \frac{\text{Height} - X}{180 - X} \times 100
\]

where:
- Height is the height of the mercury (60 mm in this case),
- X is the height of the lower fixed point.

Plugging in the values we know for when the temperature is 20°C:

\[
20 = \frac{60 - X}{180 - X} \times 100
\]

Now, let's solve for X. First, simplify the equation:

\[
20 = \frac{60 - X}{180 - X} \times 100
\]

Divide both sides by 100:

\[
0.2 = \frac{60 - X}{180 - X}
\]

Cross-multiply to eliminate the fraction:

\[
0.2(180 - X) = 60 - X
\]

Distributing gives:

\[
36 - 0.2X = 60 - X
\]

Now, let's collect like terms. Add \(0.2X\) to both sides and subtract 36 from both sides:

\[
36 - 36 = 60 - 36 - X + 0.2X
\]
\[
0 = 24 + 0.8X
\]

Now, rearranging gives:

\[
0.8X = 24
\]

Dividing both sides by 0.8:

\[
X = \frac{24}{0.8} = 30
\]

Thus, the value of X, the lower fixed point of the thermometer, is **30 mm**.