A 2.00-kg copper rod is 40.00 cm long at 23°C. If 50,000 J are transferred to the rod by heat, what is its change in length? (ccopper = 387 J/kg·°C and αcopper = 17 × 10-6/°C)Select one:a.0.022 cmb.More information is needed.c.0.044 cmd.0.055 cm
Question
A 2.00-kg copper rod is 40.00 cm long at 23°C. If 50,000 J are transferred to the rod by heat, what is its change in length? (ccopper = 387 J/kg·°C and αcopper = 17 × 10-6/°C)Select one:a.0.022 cmb.More information is needed.c.0.044 cmd.0.055 cm
Solution
First, we need to calculate the change in temperature (ΔT) using the formula Q = mcΔT, where Q is the heat transferred, m is the mass, and c is the specific heat capacity.
Rearranging the formula, we get ΔT = Q / (mc) = 50000 J / (2.00 kg * 387 J/kg·°C) = 64.6°C.
Next, we calculate the change in length (ΔL) using the formula ΔL = αLΔT, where α is the coefficient of linear expansion and L is the original length.
Substituting the values, we get ΔL = 17 × 10^-6/°C * 40.00 cm * 64.6°C = 0.044 cm.
So, the answer is c. 0.044 cm.
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