Thermal Expansion: An aluminum rod is10.0cmlong and a steel rod is80.0cmlong when both rods are at a temperature of15\\\\deg C. Both rods have the same diameter. now joined end-to-end to form a rod90.0cmlong. If the temperature is now raised from15\\\\deg Cto90\\\\deg C, what is the increase in the length of the joined rod? The coefficient of linear expansion of aluminum is2.4\\\\times 10^(-5)K^(-1)and that of steel is1.2\\\\times 10^(-5)K^(-1).\\n0.90mm\\n0.99mm\\n0.72mm\\n0.63mm\\n0.81mm
Question
Thermal Expansion: An aluminum rod is10.0cmlong and a steel rod is80.0cmlong when both rods are at a temperature of15\\deg C. Both rods have the same diameter. now joined end-to-end to form a rod90.0cmlong. If the temperature is now raised from15\\deg Cto90\\deg C, what is the increase in the length of the joined rod? The coefficient of linear expansion of aluminum is2.4\\times 10^(-5)K^(-1)and that of steel is1.2\\times 10^(-5)K^(-1).\n0.90mm\n0.99mm\n0.72mm\n0.63mm\n0.81mm
Solution
The increase in length of a material due to thermal expansion can be calculated using the formula:
ΔL = α * L * ΔT
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.
First, calculate the increase in length for the aluminum rod:
ΔL_aluminum = α_aluminum * L_aluminum * ΔT ΔL_aluminum = 2.4 * 10^(-5) K^(-1) * 10.0 cm * (90°C - 15°C) ΔL_aluminum = 0.18 cm
Next, calculate the increase in length for the steel rod:
ΔL_steel = α_steel * L_steel * ΔT ΔL_steel = 1.2 * 10^(-5) K^(-1) * 80.0 cm * (90°C - 15°C) ΔL_steel = 0.72 cm
Finally, add the increases in length for the aluminum and steel rods to find the total increase in length:
ΔL_total = ΔL_aluminum + ΔL_steel ΔL_total = 0.18 cm + 0.72 cm ΔL_total = 0.90 cm
So, the increase in the length of the joined rod is 0.90 cm, or 9.0 mm. Therefore, the correct answer is 0.90 mm.
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