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.
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
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.