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Linear expansion rod problem

  • Thread starter jsalapide
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  • #1
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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 !
 

Answers and Replies

  • #2
dx
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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.
 
  • #3
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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)

i followed your instructions and..
my answer is 71.43 degrees..
is it right???
 
  • #4
dx
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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.
 
  • #5
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tnx for the help sir.. :smile:
 
  • #6
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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?

my answer is 30.018 m..
is that correct?
 
  • #7
dx
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Yes, I get the same answer.
 
  • #8
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thanks a lot sir..
 

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