# Thermal Expansion of thermometer in ice water

• S_fabris
In summary: in summary, the mercury column in a thermometer will be different lengths depending on the temperature, but if you want to know the temperature of a solution at a certain temperature, you need to use an expansion formula.
S_fabris
Here is a two part problem I'm having trouble with:

The length of the column of mercury in a thermometer is 4cm when the thermometer is immersed in ice water and 23.5cm when the thermometer is immersed in boiled water.
a) What should be the length at room temperature 22degreesCelcius?
I did ratio calculation to find this and got 8.23cm and it was correct

Here is where I'm stuck:
b) if the mercury column is 25.2cm long when the thermometer is immersed in a chemical solution, what is the temperature of the solution (answer in deg.Celsius)

Again i tried doing a ratio: 100degC = 23.5cm
xdegC = 25.2cm
my answer was 107.23degC and I is incorrect...though it makes sense and seems correct to me logically...I'm not really sure where to go from here any advice?

Sergio

Try converting the degrees to Kelvin and see if that works.

Edit: I seem to recall an expansion formula such as L=Li*alpha*(T2-T1) where L is the initial length and Li is the length by which it changes. Alpha is a constant. Maybe try solving for T2. Don't know if this is right though.

Last edited:
Not sure what you mean by ratio.

23.5cm - 4cm = 19.5cm over 100 C, so each 1 C division is 0.195cm. Go from there

If I use this information...

0.195cm = 1 C
25.2cm = x C

so 0.195(x) = 25.2(1)
x = 25.2/0.195
x = 129.23 C (incorrect)

that what i meant by "ratio" (i study in French don't know English terms that well :P)

so so far i know that 129.23C and 107.23C are incorrect :S

(25.2cm - 23.5cm) = 1.7cm, you just need to work out how many degrees C 1.7cm represents. You then add this to 100 C ( the temperature at 23.5cm)

Your method is 'wrong' because the x=0cm doesn't represent T = 0 C it represents x= 4cm, T= 0 C.

Thanks for clearing this up for me Max (and your patience)

Something just wasn't clicking i guess...i got the correct answer at 108.72C :D

Thx again :)

## 1. How does thermal expansion affect a thermometer in ice water?

When a thermometer is placed in ice water, the molecules in the thermometer's liquid expand due to the decrease in temperature. This expansion causes the liquid to rise up the thermometer, indicating a lower temperature.

## 2. Why is the amount of thermal expansion of a thermometer important?

The amount of thermal expansion of a thermometer is important because it allows us to accurately measure and record changes in temperature. Without this expansion, the thermometer would not be able to indicate changes in temperature as accurately.

## 3. What is the relationship between temperature and thermal expansion of a thermometer?

The thermal expansion of a thermometer is directly related to the temperature. As the temperature increases, the molecules in the liquid of the thermometer will expand, causing the liquid to rise up the thermometer. As the temperature decreases, the molecules will contract, causing the liquid to lower on the thermometer.

## 4. Can thermal expansion affect the accuracy of a thermometer?

Yes, thermal expansion can affect the accuracy of a thermometer. If the thermometer is not calibrated properly or if there are external factors affecting the temperature of the thermometer, it can lead to inaccurate readings. It is important to calibrate and handle thermometers carefully to ensure accuracy.

## 5. How does thermal expansion of a thermometer differ in different substances?

The thermal expansion of a thermometer can vary depending on the substance used in the thermometer. For example, mercury thermometers have a higher coefficient of thermal expansion compared to alcohol thermometers, meaning they will expand more for the same change in temperature. Additionally, different substances have different freezing and boiling points, which can also affect the thermal expansion of the thermometer.

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