An aluminum baseball bat has a length of 0.87 m at a temperature of 20°C. When the temperature of the bat is raised, the bat lengthens by 0.00016 m. Determine the final temperature of the bat.
°C
I will be happy to critique your thinking. Use the linear coefficent of expansion for aluminum
To determine the final temperature of the bat, we can use the concept of thermal expansion.
The equation for linear expansion is given by:
ΔL = α * L * ΔT
Where:
ΔL is the change in length
α is the coefficient of linear expansion
L is the original length
ΔT is the change in temperature
In this case, we are given:
ΔL = 0.00016 m (the change in length)
L = 0.87 m (the original length)
α = coefficient of linear expansion (specific for aluminum)
ΔT = ? (the change in temperature that we need to find)
First, let's determine the coefficient of linear expansion for aluminum. The coefficient depends on the material and is usually given in units of per Celsius degree (°C^-1). For aluminum, the coefficient of linear expansion is approximately 0.0000220 °C^-1.
Now, we can rearrange the equation to solve for ΔT:
ΔT = ΔL / (α * L)
Plugging in the given values:
ΔT = 0.00016 m / (0.0000220 °C^-1 * 0.87 m)
ΔT ≈ 8.2136°C
Therefore, the final temperature of the bat is approximately 8.2136°C higher than its initial temperature of 20°C.
Final temperature = 20°C + 8.2136°C
Final temperature ≈ 28.214°C
So, the final temperature of the bat is approximately 28.214°C.