The linear expansivity of brass is 2 x 10\(^{-5}\) C\(^{-1}\). If the volume of a piece of brass is 15.00cm at 0°C, what is the volume at 100°C
16.03cm\(^3\)
15.09cm\(^3\)
16.00cm\(^3\)
15.03cm\(^3\)
Explanation
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To find the volume of the brass at 100°C, we need to consider its expansion using the formula:
ΔV = V * α * ΔT
Where:
ΔV = change in volume
V = initial volume
α = coefficient of linear expansion
ΔT = change in temperature
Given:
Initial volume (V) = 15.00 cm³
Coefficient of linear expansion (α) = 2 x 10^-5 °C^-1
Change in temperature (ΔT) = 100°C - 0°C = 100°C
Substituting the values into the formula:
ΔV = 15.00 cm³ * 2 x 10^-5 °C^-1 * 100°C
ΔV = 15.00 cm³ * 2 x 10^-3
ΔV = 0.03 cm³
Now, to find the final volume:
Final volume = Initial volume + Change in volume
Final volume = 15.00 cm³ + 0.03 cm³
Final volume = 15.03 cm³
So, the volume of the brass at 100°C is 15.03 cm³.
V2=new volume, v1=original volume
V2=v1(1 +linear expansivity of brass*temperature difference)
V2=15(1+2*10^-5*(100-0))
V2=15.03
