Question

3. Two wires increase in length by the same amount when both their temperatures increase by the same amount, as shown in the diagram. Before the temperature increase, the longer wire is 1.2525 m long. The shorter wire’s linear coefficient of thermal expansion is 1.135 times that of the longer wire. How much shorter is the shorter wire before the temperature increase? Answer to three significant figures
Viết cho Ngọc Khánh

Answer 1

Two wires increase in length by the same amount when both their temperatures increase by the same amount, the shortness of the wire before the temperature increase is mathematically given as

dL=0.1485m

How much shorter is the shorter wire before the temperature increase?

Generally, the equation for change in length is mathematically given as

$dl=lo \alpha dt$

Therefore

dl1=dl2

Where

a2=1.35a1

Hence

a1l1dt= a2l2dt

a1(1.2525)= a1*(1.135)(l2)

L2=1.104m

In conclusion, a change in length due to temperature is

dL=1.2525-1.104m

dL=0.1485m

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