Calculate the change of volume from volume expansion coefficient

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Discussion Overview

The discussion revolves around the calculation of volume change due to temperature changes using the volume expansion coefficient (β). Participants explore the implications of β, the necessary information for calculations, and specific scenarios involving mercury's volume change with temperature variations.

Discussion Character

  • Exploratory
  • Technical explanation
  • Homework-related

Main Points Raised

  • One participant questions the meaning of "v" in the equation β= (1/v)(∂v/∂T) at constant pressure, suggesting it may represent molar volume.
  • Another participant proposes that if the change in temperature is relatively small, the change in volume can be approximated using the formula: β * ΔT * V = ΔV, but notes that the definition of "relatively small" and the value of V are necessary for this calculation.
  • A participant poses a specific scenario involving mercury, asking if it is possible to calculate the volume of mercury that will spill out when heated from 0 to 50 degrees Celsius, given the β of mercury.
  • Another participant reiterates the mercury scenario and emphasizes that a 50-degree change is significant, questioning the initial volume needed for the calculation.
  • One participant states that the initial volume is not provided, implying that the question cannot be solved without it.
  • A participant rewrites the equation for volume change and integrates it, presenting a formula for volume at a new temperature based on the initial volume and temperature.

Areas of Agreement / Disagreement

Participants express uncertainty about the necessary information for calculations, particularly regarding the initial volume. There is no consensus on whether the problem can be solved without this information, and multiple viewpoints on the implications of temperature changes and the use of β are present.

Contextual Notes

The discussion highlights limitations such as the dependence on the initial volume, the definition of "relatively small" temperature changes, and the assumptions underlying the use of the volume expansion coefficient.

Outrageous
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β= (1/v)(∂v/∂T)constant pressure.
What is the v represent? molar volume?
If I am given the β and the change of temperature, how to calculate the change of volume? or it is not enough information to calculate it?

Thank you.
 
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it seems like you have enough if the change is relatively small so that you could use deltas:

beta * delta T * V =delta V

You'd have to decide on what relatively small means and you have to know what V is.
 
Thank you
Question : a container is filled with mercury at 0 degree celsius. At temperature 50 degree celsius , what is the volume of mercury that will spill out ?
β Of mercury is 18*10^(-5) /celsius

Is this possible to do ?
 
Outrageous said:
Thank you
Question : a container is filled with mercury at 0 degree celsius. At temperature 50 degree celsius , what is the volume of mercury that will spill out ?
β Of mercury is 18*10^(-5) /celsius

Is this possible to do ?

What do you think? A delta of 50 degrees is pretty significant.

What is the initial volume?
 
The initial volume is not given , so that question can't be solved?
 
Outrageous said:
β= (1/v)(∂v/∂T)constant pressure.
What is the v represent? molar volume?
If I am given the β and the change of temperature, how to calculate the change of volume? or it is not enough information to calculate it?

Thank you.

Rewriting your equation:

\frac{d\ln{v}}{dt}=\beta

Integrating, you get:

v=v_0\exp(\beta(T - T_0))

where v0 is the volume at temperature T0.
 

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