Question on: JAMB Physics - 2020
The linear expansivity of brass is 2 x 10\(^{-5}\) \(^oC^{-1}\). If the volume of piece of brass is 2 x 10cm\(^3\) at 0\(^o\)C. What will be its volume at 100\(^o\)C?
10.06cm\(^3\)
10.04 cm\(^3\)
10.02 cm\(^3\)
10.06 cm\(^3\)
The question provides the linear expansivity of brass and asks for the volume at a different temperature. We need to use the concept of volume expansivity, which is related to linear expansivity.
Here's how to solve the problem:
-
Relationship between linear and volume expansivity:
- Volume expansivity ((\gamma)) is approximately three times the linear expansivity ((\alpha)): (\gamma = 3\alpha)
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Calculate the volume expansivity:
- Given (\alpha = 2 \times 10^{-5} , ^\circ C^{-1})
- (\gamma = 3 \times (2 \times 10^{-5} , ^\circ C^{-1}) = 6 \times 10^{-5} , ^\circ C^{-1})
-
Apply the volume expansion formula:
- (\Delta V = V_0 \gamma \Delta T)
- Where:
- (\Delta V) is the change in volume
- (V_0) is the original volume ((2 \times 10) cm(^3) = 20 cm(^3))
- (\gamma) is the volume expansivity ((6 \times 10^{-5} , ^\circ C^{-1}))
- (\Delta T) is the change in temperature ((100 ^\circ C - 0 ^\circ C = 100 ^\circ C))
-
Calculate the change in volume:
- (\Delta V = (20 , cm^3) \times (6 \times 10^{-5} , ^\circ C^{-1}) \times (100 , ^\circ C))
- (\Delta V = 0.12 , cm^3)
-
Calculate the final volume:
- (V = V_0 + \Delta V)
- (V = 20 , cm^3 + 0.12 , cm^3 = 20.12 , cm^3)
Therefore, the final volume of the brass at (100 ^\circ C) is (20.12 , cm^3). None of the given options match this result.
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