If a copper wire's length increases by 1/10 of 1%, what is the change in temperature of the wire?

To determine the change in temperature of the copper wire when it increases in length, we can apply the principle of thermal expansion. The relationship between temperature change and length change for metals is described by the formula:

ΔL = α * L0 * ΔT

where ΔL is the change in length, α is the coefficient of linear expansion, L0 is the original length of the wire, and ΔT is the change in temperature.

For copper, the coefficient of linear expansion (α) is approximately 0.000017 per degree Celsius. When the wire's length increases by 1/10 of 1%, this translates to a length change of 0.001L0.

Rearranging the formula to solve for ΔT gives us:

ΔT = ΔL / (α * L0)

Substituting in our values:

ΔT = (0.001L0) / (0.000017 * L0)

The L0 cancels out, simplifying the equation to:

ΔT = 0.001 / 0.000017 ≈ 58.82°C

When rounding, this value is closest to 60.2°C. This shows that when the copper wire's length increases by