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
2007-05-14 17:14:17 · 1 answers · asked by Emma 1 in Science & Mathematics ➔ Physics
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?
;-)
2007-05-16 07:23:55 · answer #1 · answered by Edward 7 · 1⤊ 2⤋