mtimko
  • mtimko
An aluminum plug (α = 2.3 x 10-5/C°) has a diameter of 10.003 cm at 40.0 °C. At what temperature (in Celcius) will it fit precisely into a hole of constant diameter 10.000 cm?
Physics
schrodinger
  • schrodinger
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anonymous
  • anonymous
Yo can use thermal expansion for linear dimensions \[\frac{ \Delta L }{ L_0 }=\alpha \Delta T\] \[\frac{ L-L_0 }{ L_0 }=\alpha(T-T_0)\] Let \(L_0=10.003~cm\) at \(T_0=40°C\) and \(L=10.000~cm\) at unknown temperature \(T\). \[\frac{ 10.000~cm-10.003~cm }{ 10.003~cm }=(2.3 \times 10^{-5}/°C)(T - 40°C)\] fyi: http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/thexp.html#c1

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