# Linear expansion rod problem

1.An aluminum rod and a copper rod have the same length of 100 cm at 5 degrees Celsius. At what temperature would one of the rods be 0.5mm longer than the other? Which rod is longer at such temperature?

how can i solve this? i have no idea.. help !

dx
Homework Helper
Gold Member
What are the coefficients of expansion of these materials? What is the equation for the change in length in terms of the coefficient of expansion α and the change in temperature ∆T? Subtract the changes in length (larger first) of each of the rods and equate it to 0.5 mm, and solve for ∆T.

What are the coefficients of expansion of these materials? What is the equation for the change in length in terms of the coefficient of expansion α and the change in temperature ∆T? Subtract the changes in length (larger first) of each of the rods and equate it to 0.5 mm, and solve for ∆T.

the coefficient of expansion of aluminum is 2.38x10^-5
the coefficient of expansion of copper is 1.68x10^-5
the equation I used was ∆L=(α∆T)(100cm)

is it right???

dx
Homework Helper
Gold Member
Yes, that would be the change in temperature. The original temperature is 5 °C, so you must add this to the change to get the actual temperature.

tnx for the help sir.. how bout this one..

1.On a hot day where the temperature is 32 degrees celsius, the distance between two lamp posts on the road is 30m as measured by a metal tape whose coefficient of linear expansion is hypothetically 50 x 10^-6 /degree Celsius. If the tape gives its correct reading at 20 degrees, what is the actual distance between the lamp posts?