How many meters does it expand for each 1.00-Celsius degree change in temperature?

Question

A metal rod is 25.000cm long at 25.0 degrees Celsius. When heated to 102.0 degrees Celsius, it is 25.054 cm long. How many meters does it expand for each 1.00-Celsius degree change in temperature?

Answer 1

The increase in temperature was 102.0 - 25.0 = 77.0 °C. The increase in length was 25.054 - 25.000 = 0.054 cm = 0.00054 m. The increase in length per degree temperature change is therefore 0.00054 m / 77.0 °C = 0.00000701 m / °C

Answer 2

The coefficient of expansion for this elongation:

growth of rod = 0.054cm when temperature change is 77 degrees C

alpha = coefficient of expansion = growth/original length/delta temperature = 0.054/25/77 = 28.0519E-6 cm/cm/degree C

for a 100 degree temperature change the change in length of the rod = alpha*delta T*original length = 28.0519E-6*100*25 = 0.070 cm = .00070 meters