Suppose you have two meter sticks, one made of steel and one made of invar (an alloy of iron and nickel), which are the same length (1.00 m) at 0°C. The coefficients of volume expansion for steel and invar are 3.6 * 10-5 / °C and 2.7 * 10-6 / °C respectively. What is their difference in length, in meters, at 20.5°C? Repeat the calculation for two 30.0-m-long surveyor's tapes

Difference in Length of steel is 0.000246m

Difference in Length of invar is 0.00001845m

Difference in Length of steel surveyor's tape is 0.00738m

Difference in Length of invar surveyor's tape is 0.0005535m

Explanation:

Linear expansivity of steel is volume expansivity : 3

Linear expansivity of steel = 0.000036/°C : 3 = 0.000012/°C

Difference in Length of steel = Linear expansivity * initial length * temperature change

= 0.000012 * 1 * (20.5-0)

= 0.000012*1*20.5 = 0.000246m

Linear expansivity of invar = volume expansivity of invar : 3

Linear expansivity of invar = 0.0000027/°C : 3 = 0.0000009/°C

Difference in Length of invar = 0.0000009*1 * (20.5-0) = 0.00001845m

Difference in Length of steel surveyor's tape = 0.000012*30 * (20.5-0) = 0.00738m

Difference in Length of invar surveyor's tape = 0.0000009*30 * (20.5-0) = 0.0005535m