A 3.00-kg copper rod is 45.0 cm long at 24.8°C.If 45 000 J are transferred to the rod by heat,what is its change in length? c_copper = 387 J/kg⋅°C and α_copper = 17.0 × 10−⁶/°C.

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Quizplus · Accepted Answer

The change in length can be calculated using the formula for thermal expansion: ΔL = αL0ΔT, where ΔL is the change in length, α is the coefficient of linear expansion, L0 is the initial length, and ΔT is the change in temperature. First, we need to find ΔT using the heat transferred (Q = mcΔT, where m is the mass, c is the specific heat capacity, and ΔT is the change in temperature). Rearranging for ΔT gives ΔT = Q/(mc). Substituting the given values: ΔT = 45000 J / (3.00 kg * 387 J/kg°C) = 38.76°C. Then, using ΔL = αL0ΔT: ΔL = 17.0 × 10^-6 /°C * 45.0 cm * 38.76°C = 0.0297 cm.

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