Question #21598

When a 100-m metal pipe is heated from 20°C to 43.5°C, it lengthens by 4.00 cm. What type of pipe is this?

brass

aluminum

gold

copper

brass

aluminum

gold

copper

Expert's answer

Relative expansion dL/L isequal to alpha*dT, where alpha is the coefficient of linear expansion and dT is the temperature increment.

We have

L = 100 m

dl = 4 cm,

dT = (43.5 - 20) °C = 23.5 °C

Thus, we can find

alpha = dL/(L*dT) = 4*10^(-2) m / (100 m * 23.5 °C) = 1.702 * 10^(-5) 1/°C.

By referring to a table of coefficients for different metals (e.g. https://en.wikipedia.org/wiki/Thermal_expansion) we find that it's closest to that of copper.

**Answer: copper**

We have

L = 100 m

dl = 4 cm,

dT = (43.5 - 20) °C = 23.5 °C

Thus, we can find

alpha = dL/(L*dT) = 4*10^(-2) m / (100 m * 23.5 °C) = 1.702 * 10^(-5) 1/°C.

By referring to a table of coefficients for different metals (e.g. https://en.wikipedia.org/wiki/Thermal_expansion) we find that it's closest to that of copper.

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