The Exciting Concept of Thermal Expansion in Action!

How does the length of a bronze rod change when heated from 30°C to 50°C?

Given data: Original length = 0.5m, Change in temperature = 20°C, Coefficient of linear expansion for bronze = 19 x 10^-6 °C^-1.

Answer:

The length of the bronze rod after heating to 50°C, factoring in thermal expansion, is 0.50019 meters.

Explanation:

The student is curious about the concept of linear thermal expansion. The formula for linear expansion is ΔL = αLΔT, where ΔL is the change in length, α is the coefficient of linear expansion, L is the original length, and ΔT is the change in temperature.

In this case, the original length (L) is 0.5m, the change in temperature (ΔT) is 50°C - 30°C = 20°C, and the coefficient of linear expansion (α) for bronze is 19 x 10^-6 °C^-1.

Substituting the values into the formula, we get: ΔL = 19 x 10^-6 °C^-1 * 0.5m * 20°C = 0.00019m or 0.19mm. Therefore, the length of the rod when heated to 50°C would be 0.5m + 0.00019m = 0.50019m.

It's fascinating to see how materials expand when subjected to heat, showcasing the principles of physics in action!