Calculating the coefficent of volume expansion of liquid?

In summary: The coefficient of expansion for the liquid is 0.00267 and the radius of the stem is 2.5 cm. In summary, the question involves finding the coefficient of expansion and radius of a thermometer's liquid based on a 40% increase in volume when the temperature changes by 15 Celsius. The formula ΔV = VβΔT is used and the coefficient of expansion is found to be 0.00267 while the radius of the stem is 2.5 cm.
  • #1
Pinchie81
1
0
I can't seem to figure out this question.

A Thermometer is filled with unknown liquid. It has a square bulb and a stem with cylinder shape. It is found that the volume of the liquid increased by 40% when the temperature changes by 15 Celsius.
Calculate the coefficient of expansion of volume of the liquid and the radius of the stem if the liquid rises by 5 cm?
Do I need to use the formula: ΔV = VβΔT

Don't know how to tackle this question any help would be appreciated.
 
Last edited:
Physics news on Phys.org
  • #2
Pinchie81 said:
I can't seem to figure out this question.

A Thermometer is filled with unknown liquid. It has a square bulb and a stem with cylinder shape. It is found that the volume of the liquid increased by 40% when the temperature changes by 15 Celsius.
Calculate the coefficient of expansion of volume of the liquid and the radius of the stem if the liquid rises by 5 cm?
Do I need to use the formula: ΔV = VβΔT

Don't know how to tackle this question any help would be appreciated.

WOW! I am stuck on exactly same question.
Someone tried to help me with this..I thought I understand it all now but I am stuck again haha.
This might make sense to you then you can help me.
For 1st part the volume coefficient of expansionis the fractional increase in volume per unit rise in temperature. The % increase is given so change that to a fraction and divide by the rise in temperature (0.4/15 = 0.0267?? may be :S)
For the 2nd part if you know the vol of the bulb, then you can work out the increase in the actual vol of the liquids because you know it increases by 40%. The tube is a cylinder and liquid will have a vol = area of cross section x length. You know the increase in volume and you know the length so work out the area of cross section and hencethe radius.
 
  • #3
SAFiiNA said:
This might make sense to you then you can help me.
For 1st part the volume coefficient of expansionis the fractional increase in volume per unit rise in temperature. The % increase is given so change that to a fraction and divide by the rise in temperature (0.4/15 = 0.0267?? may be :S)
For the 2nd part if you know the vol of the bulb, then you can work out the increase in the actual vol of the liquids because you know it increases by 40%. The tube is a cylinder and liquid will have a vol = area of cross section x length. You know the increase in volume and you know the length so work out the area of cross section and hencethe radius.
I think you explained that very well, SAFiiNA. And judging by the absence of any further query from Pinchie81, I'd conclude that you managed to answer his/her questions! :wink:
 
  • #4
NascentOxygen said:
I think you explained that very well, SAFiiNA. And judging by the absence of any further query from Pinchie81, I'd conclude that you managed to answer his/her questions! :wink:

Thank you! :) I finally managed to work it out myself.
 
  • #5


I would suggest approaching this question by first understanding the concept of coefficient of volume expansion. This is a measure of how much a substance's volume changes when its temperature changes. The formula you mentioned, ΔV = VβΔT, is correct. Here, β represents the coefficient of volume expansion, V is the original volume of the substance, ΔV is the change in volume and ΔT is the change in temperature.

In this case, we have been given that the volume of the liquid increased by 40% when the temperature changed by 15°C. Using the formula, we can write this as 40% = β * 15°C. Solving for β, we get β = 2.67 x 10^-3 °C^-1. This is the coefficient of volume expansion for the liquid.

To calculate the radius of the stem, we need to use the formula for the volume of a cylinder, V = πr^2h, where r is the radius and h is the height (in this case, the change in height of the liquid). We know that the liquid rises by 5 cm, so h = 5 cm. We also know that the original volume of the liquid (before the temperature change) was equal to the volume of the square bulb. Therefore, we can write V = πr^2 = Vb, where Vb is the volume of the bulb. Rearranging the equation, we get r = √(Vb/π). Now, using the value of β we calculated earlier, we can plug in the values and solve for r.

I hope this helps you understand how to approach this question. It is important to have a clear understanding of the concepts involved and to use the correct formulas in order to solve problems like these.
 

What is the coefficient of volume expansion of a liquid?

The coefficient of volume expansion of a liquid is a measure of the change in volume of a liquid due to a change in temperature. It is denoted by the symbol "β" and is typically measured in units of 1/K (kelvins).

How is the coefficient of volume expansion of a liquid calculated?

The coefficient of volume expansion can be calculated using the formula β = (ΔV/VΔT), where ΔV is the change in volume, V is the initial volume, and ΔT is the change in temperature.

What factors affect the coefficient of volume expansion of a liquid?

The coefficient of volume expansion of a liquid is affected by the type of liquid, the temperature range, and the pressure. Additionally, it can also be influenced by the presence of impurities or additives in the liquid.

Why is the coefficient of volume expansion important to consider?

The coefficient of volume expansion is important because it helps us understand how a liquid will behave when exposed to changes in temperature. It is also crucial in the design and functioning of various devices and systems, such as thermometers and thermos flasks.

Can the coefficient of volume expansion change?

Yes, the coefficient of volume expansion can change depending on the factors mentioned above. For example, the coefficient of volume expansion of water is different at different temperatures. Additionally, adding impurities to a liquid can also alter its coefficient of volume expansion.

Similar threads

  • Advanced Physics Homework Help
Replies
5
Views
906
  • Mechanical Engineering
Replies
4
Views
2K
  • Thermodynamics
Replies
6
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
464
  • Engineering and Comp Sci Homework Help
Replies
31
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
2K
  • General Engineering
Replies
6
Views
2K
  • Introductory Physics Homework Help
Replies
4
Views
11K
  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
1K
Back
Top