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The length of an iron rod is 2m at 0°C, and its cubical expansivity is 12×10 ⁻⁶K⁻¹ . Its length at 50°C will be… and why?

User Alaboudi
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Final answer:

An iron rod with an original length of 2m at 0°C and a cubical expansivity of 12×10⁻⁶K⁻¹ will measure 2.0012m at 50°C. This lengthening occurs due to thermal expansion when the rod's temperature is raised.

Step-by-step explanation:

The length of an iron rod at 50°C, if it measures 2 meters at 0°C and has a cubical expansivity of 12×10⁻⁶K⁻¹, can be calculated using the formula for linear thermal expansion, ΔL = αLΔT. Here, ΔL represents the change in length, α is the coefficient of linear expansion, L is the original length, and ΔT is the change in temperature. Given that the original length (L) is 2 meters, the temperature change (ΔT) is 50°C, and the expansion coefficient (α) is 12×10⁻⁶K⁻¹, we apply the values to the formula:

ΔL = αLΔT = (12×10⁻⁶K⁻¹)(2m)(50K) = 0.0012 meters.

This results in an additional length of 0.0012 meters. Therefore, the new length of the rod at 50°C will be:

2m + 0.0012m = 2.0012m.

Thus, the increased temperature causes the iron rod to expand as a result of thermal expansion.

User Pi
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