If a brass sphere with a diameter of 16. 0 cm at 68°F is heated up to a temperature of 284°F. The change in volume of the sphere is 14.67
.
Given,
Diameter of the sphere (d) = 16.0 cm
∴ radius of the sphere (r) = ![\frac{16}{2} =8 cm](https://tex.z-dn.net/?f=%5Cfrac%7B16%7D%7B2%7D%20%3D8%20cm)
Initial temperature of the sphere
° F and final temperature
°F
Converting temperature from fahrenheit to celcius scale using the relation,
![C= \frac{(F-32)*5}{9}](https://tex.z-dn.net/?f=C%3D%20%5Cfrac%7B%28F-32%29%2A5%7D%7B9%7D)
∴
°C
°C
∴Temperature difference ΔT =
°C
Now, the co-efficient of linear expansion for brass
\°C
Hence, co-efficient of volume expansion
\°C
∴ Initial volume of the sphere,
![V_{1}=\frac{4}{3}\pi r^{3}](https://tex.z-dn.net/?f=V_%7B1%7D%3D%5Cfrac%7B4%7D%7B3%7D%5Cpi%20r%5E%7B3%7D)
⇒![V_{1}= \frac{4}{3}\pi (8)^{3}=2144.66 cm^{3}](https://tex.z-dn.net/?f=V_%7B1%7D%3D%20%5Cfrac%7B4%7D%7B3%7D%5Cpi%20%288%29%5E%7B3%7D%3D2144.66%20cm%5E%7B3%7D)
∴The change in volume at 140°C is,
ΔV![=\gamma V_{1}\Delta T](https://tex.z-dn.net/?f=%3D%5Cgamma%20V_%7B1%7D%5CDelta%20T)
⇒![\Delta V= (3*19*10^{-6})*2144.66*120](https://tex.z-dn.net/?f=%5CDelta%20V%3D%20%283%2A19%2A10%5E%7B-6%7D%29%2A2144.66%2A120)
⇒![\Delta V= 14.67 cm^{3}](https://tex.z-dn.net/?f=%5CDelta%20V%3D%2014.67%20cm%5E%7B3%7D)
∴ If the sphere is heated up to a temperature of 284°F. The change in volume of the sphere is 14.67
.
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