Question

Suppose a meter stick made of steel and one made of invar are the same length at 0°C. What is their difference in length at 59.5°C? The coefficient of thermal expansion is 12 ✕ 10−6/°C for steel and 0.9 ✕ 10−6/°C for invar. mm

(b) Repeat the calculation for two 34.5-m-long surveyor's tapes. mm

Answer 1

a) Change in length is given by

$\Delta L=L*\Delta T*(\alpha _{s}-\alpha _{i})$    (1)

where L is the length = 1m ,
VI
is the change in temperature=59.5⁰C, $\alpha _{S}$ is thermal expansion coefficient of steel =12x10^-6/⁰C, $\alpha _{i}$ is thermal expansion coefficient of ivar= 0.9 ✕ 10^-6/°C

substitute

$\Delta L=1*59.6*(12*10^{-6}-0.9*10^{-6})=6.6*10^{-4}m$

b) here only change is length of the tape 34.5 m substitute in (1)

$\Delta L=34.5*59.6*(12*10^{-6}-0.9*10^{-6})=6.6*10^{-4}m=0.02m$