Linear thermal expansion, a space between two metal rods

  • #1
Problem: The brass bar and the aluminum bar are each attached to an immovable wall. At 21.8 °C the air gap between the rods is 1.33 x 10-3 m. At what temperature will the gap be closed? length of brass is 2.0 meters, aluminum is 1.o meters


Why my solution isnt working I'm not entirely sure, but I feel it may simply be errors in my calculus.



The attempt at a solution
aAlum= 23E-6 aBrass=19E-6

23E-6(1.0)chngT+19E-6(2.0)chngT=1.33E-3m
chngT(23E-6(1.0)+19E-6(2.0))=1.33E-3m
chngT=1.33E-3m/((23E-6(1.0)+19E-6(2.0))
chngT=20.78125
21.80+20.78125=42.58125C
 

Answers and Replies

  • #2
Final Temperature : T
Initial Temperature : 21.8°C
Air gap between the rod/ Changes in Length of brass & aluminium bar: 1.33e-3m

Delta length of Brass + Delta length in Aluminium = 1.33e-3m
19e-6 x 2 x ( T-28) + 23e-6 x 1 x (T-28) = 1.33e-3m
6.1e-5T = 3.008e-3
T=49.31°C #
 

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