Volume Thermal Expansion Question ?

In summary: Also, remember that the values given for the thermal expansion coefficients are per degree Celsius, so you do not need to multiply by the temperature change of 12 degrees.In summary, we are asked to find the volume of mercury that spills out of a hole in a brass shell when the temperature is increased by 12 degrees Celsius. To solve this, we use the thermal expansion coefficients of brass, mercury, and steel to calculate the change in volume of each material and then find the difference between the change in mercury volume and the change in interior volume. After careful calculations, we find that the spillover volume is approximately 5.70 x 10^-7 m^3.
  • #1
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Volume Thermal Expansion Question!??

a spherical brass shell has an interior volume of 1.60 x 10^-3 m^3. Within this interior volume is a solid steel ball that has a volume of 0.70 x 10^-3 m^3. The space between the steel ball and the inner surface of the brass shell is filled completely with mercury. A small hole is drilled through the brass, and the temperature of the arrangement is increased by 12 degrees celsius. What is the volume of the mercury that spills out of the hole?

B(brass) = 57 x 10^-6 (degrees celsius)^-1
B(mercury) = 182 x 10^-6 (degrees celsius)^-1
B(steel) = 36 x 10^-6 (degrees celsius)^-1

My Approach:

Change in Velocity = mercury(BVchangeT) - steel(BVchangeT) - brass(BVchangeT)

= (1.6 x 10^-3 - 0.7 x 10^-3)m^3 (182 x 10^-6 celsius^-1)(12 celsius) - (36 x 10^-6 celsius^-1) (0.7 x 10 m^3)(12 celsius) - (1.60 x 10^-3 m^3)( 57 x 10^-6 celsius^-1)(12 celsius)

= 5.70 x 10^.7 m^3

Let Me know if this number is right. I really struggled on this one...kinda tricky for me!
 
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  • #2
cheechnchong said:
My Approach:

Change in Velocity = mercury(BVchangeT) - steel(BVchangeT) - brass(BVchangeT)
I assume you meant volume, not velocity!

In any case, you want to compare the increase in volume of the mercury to the increase of volume of the space between steel ball and brass shell: spillover volume = change in mercury volume - change in interior volume.

That change in interior volume is given by: change in brass volume - change in steel volume. Rewrite your equation, being more careful with your signs.
 
  • #3


I would first confirm that the given values for the thermal expansion coefficients (B) for brass, mercury, and steel are correct. Then, I would use the given formula for thermal expansion to calculate the change in volume of each material at a temperature increase of 12 degrees Celsius. This would give me the change in volume for each material, which I would then use to calculate the total change in volume of the arrangement.

Next, I would subtract the volume of the steel ball from the total change in volume to get the volume of the mercury that spilled out of the hole. This is because the steel ball is taking up space within the brass shell, so it would not contribute to the spilled mercury.

Finally, I would double-check my calculations and units to ensure accuracy. If the given values and formula were correct, then the calculated volume of spilled mercury should be accurate as well. If the number does not seem correct, I would go back and check my calculations and units to identify any errors.
 

What is volume thermal expansion?

Volume thermal expansion is the increase in volume of a substance as its temperature increases. This is due to the molecules within the substance moving farther apart, causing the substance to expand.

What factors affect volume thermal expansion?

The amount of expansion of a substance due to temperature changes depends on the substance's coefficient of volume thermal expansion, which is specific to each material. Other factors that can affect volume thermal expansion include the temperature change, the initial volume of the substance, and the pressure at which the substance is held.

How is volume thermal expansion measured?

Volume thermal expansion is typically measured using a dilatometer, which consists of a container holding the substance and a measuring device that tracks the change in volume as the temperature changes. The coefficient of volume thermal expansion can then be calculated using the initial volume, final volume, and temperature change.

What is the difference between linear and volume thermal expansion?

Linear thermal expansion refers to the increase in length of a substance as its temperature increases. Volume thermal expansion, on the other hand, refers to the increase in volume of a substance as its temperature increases. While linear thermal expansion is dependent on the length of the substance, volume thermal expansion is dependent on the initial volume of the substance.

Why is volume thermal expansion important to understand?

Understanding volume thermal expansion is important in many industries, such as construction and engineering, as it allows for the proper design and maintenance of structures and equipment. It is also important in the production of materials, as changes in volume can affect the quality and functionality of products. Additionally, volume thermal expansion is a key concept in thermodynamics and can help explain various natural phenomena, such as the expansion of water when it freezes.

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