an aluminium sphere of 20cm diameter is heated from 0¡ãc to100¡ãc. what is the change in its volume?
To find the change in volume of an aluminum sphere when heated from 0°C to 100°C, we need to use the coefficient of linear expansion for aluminum and the formula for the change in volume of a solid.
The coefficient of linear expansion (α) for aluminum is 0.000022/°C. This means that for every 1°C increase in temperature, the length of aluminum will increase by 0.000022 times its original length.
First, let's calculate the initial volume (V₁) of the aluminum sphere with a diameter of 20 cm:
Radius (r₁) = Diameter ÷ 2 = 20 cm ÷ 2 = 10 cm = 0.1 m
V₁ = (4/3) × π × r₁³
Next, let's calculate the final volume (V₂) of the aluminum sphere when heated to 100°C:
In order to do this, we need to calculate the new radius (r₂) after the temperature increase.
Change in temperature (ΔT) = Final temperature - Initial temperature = 100°C - 0°C = 100°C
Δr = α × r₁ × ΔT
r₂ = r₁ + Δr
Once we have the final radius (r₂), we can calculate the final volume (V₂) using the same formula as before:
V₂ = (4/3) × π × r₂³
Finally, we can find the change in volume (ΔV) by subtracting the initial volume from the final volume:
ΔV = V₂ - V₁
Performing the calculations should give you the desired answer.