Answer :
Final Answer:
The fractional change in volume when the temperature of a copper cube is increased by 35.0°C, with a linear coefficient of thermal expansion of [tex]17.0 × 10^-6/°C, is 2.33 × 10^-3.[/tex]
Explanation:
When a material is subjected to a change in temperature, it undergoes thermal expansion or contraction. In this case, we are dealing with a copper cube, and we need to find the fractional change in volume. To do this, we can use the formula for linear thermal expansion:
ΔL = α * L0 * ΔT
Where:
ΔL is the change in length,
α is the linear coefficient of thermal expansion (given as 17.0 × [tex]10^-6[/tex]/°C for copper),
L0 is the original length of the cube, and
ΔT is the change in temperature (given as 35.0°C).
Now, to find the change in volume, we can use the formula for volume, which depends on the cube's sides:
V = [tex]L^3[/tex]
So, the fractional change in volume (ΔV/V) is:
ΔV/V = [tex][(ΔL/L0)^3][/tex]
Substituting the values we have:
ΔV/V = [(α * ΔT)^3]
ΔV/V =[tex][(17.0 × 10^-6/°C * 35.0°C)^3][/tex]
ΔV/V =[tex](0.00000595)^3[/tex]
ΔV/V ≈ [tex]2.33 × 10^3[/tex]
So, the fractional change in volume is approximately [tex]2.33 × 10^-3.[/tex]
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