brass measuring tape is correct at 20 degree Celsius. The value 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 =1.8 ×10 raise to power minus five per Kelvin.
Thanks
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, we need to calculate the change in temperature. We know that the initial temperature (T₁) is 20 degrees Celsius and the final temperature (T₂) is 50 degrees Celsius. To convert Celsius to Kelvin, we need to add 273 to each value. Therefore, T₁ = 20 + 273 = 293 K and T₂ = 50 + 273 = 323 K.
Next, we can calculate the change in length (ΔL) using the linear expansivity formula:
ΔL = αL₀ΔT
where ΔL is the change in length, α is the linear expansivity of brass, L₀ is the initial length, and ΔT is the change in temperature.
Given that the linear expansivity of brass (α) is 1.8 × 10^(-5) per Kelvin, and we are measuring the length at an initial temperature of 20 degrees Celsius (L₀ = 70.5m), and a change in temperature of 30 degrees Celsius (ΔT = 50 - 20), we can substitute these values into the formula:
ΔL = (1.8 × 10^(-5)) × (70.5) × (30)
Now we can calculate ΔL:
ΔL = (1.8 × 10^(-5)) × (70.5) × (30) = 0.09135 meters
The positive sign indicates that the length of the measuring tape has increased due to the increase in temperature.
Finally, to find the true length of the field, we can add the change in length (ΔL) to the measured length with the rule at 50 degrees Celsius:
True length = Measured length + ΔL = 70.5m + 0.09135m = 70.59135m
Therefore, the true length of the field is approximately 70.59135 meters.