# Linear expansion rod problem

• jsalapide
In summary, the length of an aluminum rod and a copper rod at 5 degrees Celsius is 100 cm. To find the temperature at which one rod will be 0.5 mm longer than the other, we must use the coefficients of expansion (2.38x10^-5 for aluminum and 1.68x10^-5 for copper) and the equation ∆L=(α∆T)(100cm). After solving, the temperature is 71.43 degrees Celsius. Similarly, on a hot day where the temperature is 32 degrees Celsius, the distance between two lamp posts on the road is 30.018 m, taking into account the coefficient of linear expansion of the metal tape (50

#### jsalapide

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 !

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?

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?