Volume Expansion: 15.5cm Sphere Heated from 40°C to 210°C

In summary, the problem involves finding the change in volume of a quartz sphere with a diameter of 15.5 cm when heated from 40°C to 210°C. By using the formula for volume and the given information, the volume was calculated to be 15598.53 cm^3. The formula for change in volume, \Delta(V) = \beta V_o\Delta(T), was then used with a change in temperature of 170°C. The \beta value for quartz is 0.000001, but the final answer of 2.65 cm^3 is not matching with previous calculations. Further assistance may be needed to find the correct answer.
  • #1
ISU20CpreE
69
0
A quartz sphere is 15.5 cm in diameter. What will be its change in
volume if it is heated from 40°C to 210°C?
Ok so what I did was use the diameter of the sphere and use the volume formula of the sphere and I got 15598.53 cm^3. Then what I did was use this formula [tex] \Delta(V) = \beta V_o\Delta(T) [/tex] knowing this formula I plug in the informationg given in the problem, but the part I don't understand is if its [tex]\Delta(T) [/tex] shouldn't it be the final tamperature minus the initial? Giving me 170 C. I can't do that part I need help.
 
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  • #2
Yes, [tex]\Delta(T) [/tex] is the change in temperature, 170 degrees Centigrade. What do you mean you "can't do that part"? Have you looked up [itex]\beta[/itex] for quartz?
 
  • #3
HallsofIvy said:
Yes, [tex]\Delta(T) [/tex] is the change in temperature, 170 degrees Centigrade. What do you mean you "can't do that part"? Have you looked up [itex]\beta[/itex] for quartz?
YEs i did but i really can't get the answer the Beta for quartz is 0.000001 i don't get the answer right. What can i do?
 
  • #4
ISU20CpreE said:
YEs i did but i really can't get the answer the Beta for quartz is 0.000001 i don't get the answer right. What can i do?

I get 2.65 cm^3 as an answer.
 
  • #5
ISU20CpreE said:
I get 2.65 cm^3 as an answer.

is this answer corect?
 

1. How does heating affect the volume of a sphere?

Heating a sphere causes its volume to expand. This is known as thermal expansion, where the particles in a substance gain energy and move farther apart, resulting in an increase in volume.

2. What is the formula for calculating volume expansion?

The formula for volume expansion is V2 = V1 (1 + αΔT), where V2 is the final volume, V1 is the initial volume, α is the coefficient of thermal expansion, and ΔT is the change in temperature.

3. How do you calculate the change in volume of a sphere when heated?

To calculate the change in volume of a sphere when heated, you can use the formula ΔV = V0 α ΔT, where ΔV is the change in volume, V0 is the initial volume, α is the coefficient of thermal expansion, and ΔT is the change in temperature.

4. What is the coefficient of thermal expansion for a sphere?

The coefficient of thermal expansion for a sphere depends on the material it is made of. This value is typically given in units of 1/K (kelvin) or 1/°C (degrees Celsius). Common materials have coefficients of thermal expansion ranging from 10^-5 to 10^-6.

5. How much will the volume of a 15.5cm sphere change when heated from 40°C to 210°C?

To calculate the change in volume, we need the initial volume, coefficient of thermal expansion, and change in temperature. Assuming the coefficient of thermal expansion is 10^-5 and the initial volume is 15.5cm^3, the change in volume can be calculated as ΔV = 15.5cm^3 * 10^-5 * (210°C - 40°C) = 0.124cm^3. Therefore, the volume of the sphere will increase by 0.124cm^3 when heated from 40°C to 210°C.

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