A circular hole in an aluminum plate is 2.725 cm in diameter at 0.000 degrees celsius. What is its diameter when the temperature of the plate is raised to 100.0 degrees celsius?
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To find the diameter of the hole when the temperature of the plate is raised to 100.0 degrees Celsius, we can use the concept of thermal expansion. The formula to calculate thermal expansion is:
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 need to find the change in diameter, so we can use the formula:
ΔD = α * D * ΔT
Where:
ΔD is the change in diameter
D is the original diameter
We need to find the change in diameter, so ΔD can be calculated as:
ΔD = α * D * ΔT
Given:
D = 2.725 cm (original diameter)
ΔT = 100.0 - 0.0 = 100.0 °C (change in temperature)
Now, we need the coefficient of linear expansion (α) for aluminum. The coefficient of linear expansion for aluminum is approximately 0.0000225 per degree Celsius.
Substituting the values into the formula, we get:
ΔD = 0.0000225 * 2.725 * 100.0
Calculating this expression gives:
ΔD ≈ 0.000613125 cm
To find the final diameter (D_f), we can add the change in diameter (ΔD) to the original diameter (D):
D_f = D + ΔD
Substituting the values, we get:
D_f ≈ 2.725 + 0.000613125
Calculating this expression gives:
D_f ≈ 2.725613125 cm
Therefore, when the temperature of the plate is raised to 100.0 degrees Celsius, the diameter of the hole in the aluminum plate would be approximately 2.725613125 cm.
To find the diameter of the circular hole at 100.0 degrees Celsius, we need to take into account the thermal expansion of the aluminum plate.
The formula to calculate linear thermal expansion is:
ΔL = α * L * ΔT
Where:
ΔL is the change in length,
α is the coefficient of linear expansion,
L is the initial length, and
ΔT is the change in temperature.
In this case, to find the change in diameter, we can use the following formula:
ΔD = α * D * ΔT
Where:
ΔD is the change in diameter,
α is the coefficient of linear expansion,
D is the initial diameter, and
ΔT is the change in temperature.
The coefficient of linear expansion for aluminum is approximately 0.0000225 (1/°C).
Given:
Initial diameter (D) = 2.725 cm = 0.02725 m
Change in temperature (ΔT) = 100.0 °C - 0.0 °C = 100.0 °C
Coefficient of linear expansion (α) = 0.0000225 (1/°C)
Now we can substitute these values into the formula to find the change in diameter:
ΔD = α * D * ΔT
ΔD = 0.0000225 * 0.02725 * 100.0
Calculating the above expression, we get:
ΔD ≈ 0.00006069625 m
Finally, to find the diameter at 100.0 °C, we need to add the change in diameter to the initial diameter:
New Diameter = Initial Diameter + ΔD
New Diameter = 0.02725 + 0.00006069625
Calculating the above expression, we get:
New Diameter ≈ 0.02731069625 m
Therefore, the diameter of the circular hole at 100.0 degrees Celsius is approximately 0.02731069625 meters.
the hole gets bigger.
deltaDiameter=OrigDiameter*coeffexpan*deltaTemp
so the new diamter=origDiameter+deltaDiameter.