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.
To determine the final temperature of the bat, we can use the thermal expansion equation:
ΔL = α * L * ΔT
Where:
ΔL = Change in length of the bat
α = Coefficient of linear expansion for aluminum (approximately 0.000022/°C)
L = Original length of the bat
ΔT = Change in temperature
Given data:
Original length of the bat (L) = 0.87 m
Change in length of the bat (ΔL) = 0.00016 m
Rearranging the equation, we can solve for ΔT:
ΔT = ΔL / (α * L)
Substituting the given values:
ΔT = 0.00016 m / (0.000022/°C * 0.87 m)
ΔT ≈ 827.27 °C
Therefore, the final temperature of the bat is approximately 827.27 °C.
To determine the final temperature of the bat, we can use the equation for linear thermal expansion:
ΔL = α * L * ΔT
where:
ΔL is the change in length
α is the coefficient of linear expansion
L is the initial length of the bat
ΔT is the change in temperature
We are given that the initial length of the bat (L) is 0.87 m and the change in length (ΔL) is 0.00016 m. We also know that aluminum has a coefficient of linear expansion (α) of 0.000022/°C.
By substituting these values into the equation, we can solve for ΔT:
0.00016 = (0.000022/°C) * 0.87 * ΔT
Simplifying the equation gives:
ΔT = 0.00016 / [(0.000022/°C) * 0.87]
Calculating this expression will give us the change in temperature (ΔT). By adding ΔT to the initial temperature of 20°C, we can find the final temperature of the bat.
change in length/length = alpha * change in temp
alpha for aluminum = coef of linear expansion = 2.4*10^-5
so
1.6*10^-4/.87 = 2.4*10^-5 (T-20)
.766 *10^1 = T-20
T = 20 +7.66 = 27.7 deg C