A brass measuring tape is correct at 20 degree Celsius. The volume obtained when the length of a field is measured with the rule at 50 degree Celsius appears to be 70.5m. What is the true length of the field? Linear expansivity of brass is = 1.8 X 10^-5/k
using linear expansivity formula
a= change in length/ initial length * change in temperature
making initial length subject of the formula
L1 = l2/ 1+ adt
L1= 70.5/1+1.8*10^-5* (50-20)
L1 = 70.46
Student
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To find the true length of the field, we need to take into account the expansion of the brass measuring tape due to the change in temperature.
First, let's calculate the increase in length of the measuring tape due to the temperature change. We can use the linear expansion formula:
ΔL = α * L0 * ΔT
Where:
ΔL is the change in length
α is the linear expansivity of brass (given as 1.8 x 10^-5 / K for this case)
L0 is the original length of the tape
ΔT is the change in temperature (difference between the measurement temperature and the correct temperature)
Given that the measuring tape is correct at 20 degrees Celsius and measured at 50 degrees Celsius, the ΔT is 50 - 20 = 30 degrees Celsius.
Now, substituting the values into the formula:
ΔL = (1.8 x 10^-5 / K) * L0 * 30
Next, we need to find the corrected length of the field. Since the measured length of the field appears to be 70.5m, we can find the true length by subtracting the change in length from the measured length:
True Length = Measured Length - ΔL
True Length = 70.5m - [(1.8 x 10^-5 / K) * L0 * 30]
Note: We can't determine the actual value of True Length without the original length of the measuring tape (L0). However, using the given formula and information, this is the overall process and approach to finding the true length of the field.
Student
Volume???
70.5=L(1+1.8e-5*50)
solve for Length L