Question

What difference in temperature from standard, neglected in use of a steel tape, will cause an error of 1 part in 7000? Express the answer in degrees Fahrenhalt to three significant figures.

Answer 1

To calculate the temperature difference that would cause an error of 1 part in 7000, use the formula ΔT = (ΔL / L) / α, where ΔT is the temperature difference, ΔL is the change in length, L is the actual length, and α is the coefficient of linear expansion. Convert the result from Celsius to Fahrenheit by multiplying by 9/5 and adding 32.

Step-by-step explanation:

To calculate the difference in temperature that would cause an error of 1 part in 7000, we can use the formula:

ΔT = (ΔL / L) / α

Where ΔT is the difference in temperature, ΔL is the change in length of the steel tape, L is the actual length of the steel tape, and α is the coefficient of linear expansion of the steel.

Since the error is given as 1 part in 7000, we can substitute ΔL / L = 1 / 7000 into the formula and solve for ΔT.

ΔT = (1 / 7000) / α

Given that 1 °F = 5/9 °C, we can convert the answer from Celsius to Fahrenheit by multiplying by 9/5 and adding 32.