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deff fn [24]
2 years ago
15

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 water? (b) What is the temperature if the length of the rod is 6.3689 cm?
Physics
1 answer:
bezimeni [28]2 years ago
8 0

Answer:

a)6.318\ \rm m

b144.89^\circ

Explanation:

Given :

  • Length of the aluminium alloy at 16^\circ =L_1=6.3243\ \rm \ m
  • Length of the aluminium alloy at 100^\circ =L_2=6.3568\ \rm \ m

Let \alpha be the coefficient of linear thermal expansion of aluminium alloy

When the temperate of the rod is increased then its length will be changed accordingly. Let l_0 be its length at freezing point of water at T=0^\circ

l_1=l(1+\alpha \Delta T)\\\\\dfrac{l_1}{l}-1=\alpha \Delta T

According to question we have

a)

\dfrac{6.3243}{l}-1=\alpha (16-0)\\\dfrac{6.3568}{l}-1=\alpha (100-0)

Solving above two equations we get

l=6.318\ \rm m

b) Let t^\circ be the temperature of the rod when its length is 6.3689 m then we have

\dfrac{6.3689}{6.2838}-1=\alpha(t-0)

Also we have

\dfrac{6.3243}{6.318}-1=\alpha (16-0)

Solving above two equations we have

t=144.89^\circ

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