An aluminum alloy rod has a length of 6.3243 cm at 16.00°C and a length of 6.3568 cm at the boiling point of water. (a) What is the length of the rod at the freezing point of wa…

Question

asked Aug 21, 2020 179k views

1 Answer

Kawerewagaba · Answer 1 · 2020-08-28T08:25:48+0000

Answer:

Part a)

L_o = 6.3181 cm

Part b)

T = 131.3 ^oC

Step-by-step explanation:

Let the length of the rod at 0 degree Celsius is given as Lo

now we have

$L = L_o( 1 + \alpha \Delta T)$

now we know that

L_o = Length of rod at zero degree C

Part a)

$6.3243 = L_o(1 + \alpha (16 - 0))$

$6.3568 = L_o(1 + \alpha (100 - 0))$

now we have

$(6.3568)/(6.3243) = (1 + 100 \alpha)/(1 + 16 \alpha)$

$1.005(1 + 16 \alpha) = 1 + 100 \alpha$

$83.918\alpha = 5.138* 10^(-3)$

$\alpha = 6.12 * 10^(-5)$

now we have

L_o = 6.3181 cm

Part b)

length of the rod is 6.3689 cm

now we have

$L = L_o(1 + \alpha\Delta T)$

$6.3689 = 6.3181(1 + \alpha \Delta T)$

6.3689 = 6.3181(1 + (6.12 * 10^(-5))(T - 0))

1.008 = 1 + (6.12 * 10^(-5))T

T = 131.3 ^oC