An aluminum rod is 10.0 cm long and a steel rod is 80.0 cm long when both rods are at a temperature of 15°C.Both rods have the same diameter.The rods are now joined end-to-end to form a rod 90.0 cm long.If the temperature is now raised from 15°C to 90°C,what is the increase in the length of the joined rod? The coefficient of linear expansion of aluminum is 2.4 × 10^-5 K^-1 and that of steel is 1.2 × 10^-5 K^-1.

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Quizplus · Accepted Answer

The increase in length of the aluminum rod is:$$\Delta L_{Al} = \alpha_{Al} L_{Al} \Delta T = (2.4 	imes 10^{-5} K^{-1})(0.100 m)(90°C - 15°C) = 1.68 	imes 10^{-3} m$$The increase in length of the steel rod is:$$\Delta L_{steel} = \alpha_{steel} L_{steel} \Delta T = (1.2 	imes 10^{-5} K^{-1})(0.800 m)(90°C - 15°C) = 8.64 	imes 10^{-3} m$$The total increase in length of the joined rod is:$$\Delta L_{total} = \Delta L_{Al} + \Delta L_{steel} = 1.68 	imes 10^{-3} m + 8.64 	imes 10^{-3} m = 1.032 	imes 10^{-2} m = 10.32 mm$$Therefore, the increase in the length of the joined rod is 10.32 mm, which is closest to choice A) 0.90 mm.

An Aluminum Rod Is 10