Final answer:
To find the change in volume of the steel ball when the temperature is increased, we can use the formula for thermal expansion. Substituting the given values into the formula, the change in volume is calculated to be approximately 0.00000891 cm³.
Step-by-step explanation:
In order to calculate the change in volume of the steel ball when the temperature is increased, we need to use the formula for thermal expansion. The formula is given by:
ΔV = βVΔT
where ΔV is the change in volume, β is the coefficient of volume expansion, V is the initial volume, and ΔT is the change in temperature.
Since we are given the initial volume (V₁ = 15.3 cm³) and the initial temperature (T₁ = 35˚C), we need to find the coefficient of volume expansion (β) for steel. The coefficient of volume expansion for steel is approximately 12 x 10^(-6) K^(-1).
Using the values in the formula, we can calculate the change in volume:
ΔV = (12 x 10^(-6) K^(-1))(15.3 cm³)(84.5°C - 35°C)
Simplifying the equation:
ΔV = 12 x 10^(-6) K^(-1) x 15.3 cm³ x 49.5°C
ΔV = 0.00000891 cm³
Therefore, the change in volume of the steel ball when the temperature is increased to 84.5°C is approximately 0.00000891 cm³.