Answer to Question #86664 in Molecular Physics | Thermodynamics for Udeh George

Question

A metal tape correct at 30 degrees is used to measure the length of field on a day when the temperature is 20 degrees. How does this affect the result.? What is the error measuring a distance of 10meters? The linear expansivity of the metal is 18x10 raise to power of - 6 per k.

Answer 1

The linear thermal contraction of metal tape

$$\Delta l=l_0\alpha\Delta T$$ $$=(1\:\rm{m})\times(18\times10^{-6}\:\rm{K^{-1}})\times (10\:\rm{K})=18\times10^{-5}\:\rm{m}$$

So, the error measuring a distance of 10 m is

$$\rm{error}=(10\:\rm{m})\times(18\times10^{-5}\:\rm{m})=18\times10^{-4}\:\rm{m}=1.8\:\rm{mm}$$