Brass Ring
February 28th, 2011
Brain Teaser!! Brass ring, aluminum rod and temperature.. Can someone please help me! the more the merrier!!?
A brass ring of diameter 10.00 cm at 19.0°C is heated and slipped over an aluminum rod with a diameter of 10.01 cm at 19.0°C. Assuming the average coefficients of linear expansion are constant.
(a) To what temperature must this combination be cooled to separate the two metals?
________C
Is this temperature attainable?
yes
(b) To what temperature must this combination be cooled to separate the two metals if the aluminium rod were 10.05 cm in diameter?
_________°C
Aluminum23 E-6/K at 20 °C
Brass 19 E-6/K at 20 °C
L1A – L2A=L1A Ca (T1-T2)
L1B – L2A=L1B CB (T1-T2)
Subject to condition L2A=L2B=L
we have
L=L1A – L1A Ca (T1-T2)
L=L1B – L1B Cb (T1-T2)
Subtracting we have
0= (L1A – L1B) – (T1-T2) (L1A Ca – L1B Cb )
T1-T2= (L1A – L1B) / (L1A Ca – L1B Cb )
T2= T- (L1A – L1B) / (L1A Ca – L1B Cb )
T2= 19.0 – (10.00 – 10.01) / [(10.00 x 19 - 10.01 x 23) x 1E-6]
T2= -248.6 C
Absolute zero is 0K or -273.15C
It is achievable.
(b) Use the same equation but now L1A= 10.05 cm
But is it attainable?
THE BRASS RING – “The Dis-Advantages Of You” (1967)
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