I have the right answers but dont know how to getthem. An aluminum-alloy rod has
ID: 1729703 • Letter: I
Question
I have the right answers but dont know how to getthem.An aluminum-alloy rod has a length of 10.006 cm at 19.400°C and a length of 10.023 cm at the boiling point of water. (a) What is the length of the rod at thefreezing point of water? (Answer to the nearest 0.001 cm.)10.002cm
(b) What is the temperature if the length of the rod is10.020 cm? 85.9°C I have the right answers but dont know how to getthem.
An aluminum-alloy rod has a length of 10.006 cm at 19.400°C and a length of 10.023 cm at the boiling point of water. (a) What is the length of the rod at thefreezing point of water? (Answer to the nearest 0.001 cm.)10.002cm
(b) What is the temperature if the length of the rod is10.020 cm? 85.9°C
Explanation / Answer
Length of aluminum-alloy rodat 19.4 oC, L1 = 10.006 cm Length ofaluminum-alloy rod at 100 oC, L2 = 10.023 cm Freezing point ofwater = 0 oC (a) Coefficient of linear expansion, = ( L2 - L1 ) / L1t = 0.017 / ( 10.006 * 80.6 ) = 2.11 X 10 -5 / oC Length of water at freezing point of water, L' = L1 ( 1 + t ) = 10.006 [ 1 + 2.11 X 10 -5 * ( 0 - 19.5 ) ] = 10.006 * 0.99959 = 10.002 cm ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ (b) Initial length, L1 = 10.006 cm Initial temperature, t1 = 19.5 oC Newlength, L2 = 10.02 cm Newtemperature, t2 = ? Newtemperature, t2 = t1 + [ ( L2 - L1 ) / L1 ] = 19.5 + [ 0.014 / ( 2.11 X 10 -5 * 10.006 ] = 19.5 + 66.3 = 85.8 oC