Physics

Problem

A solid cylindrical copper rod of length

0.25\,\text{m}

is meant to conduct

1.0\times10^{3}\,\text{W}

of thermal energy from an engine block at

200\,^{\circ}\text{C}

to a coolant reservoir at

50\,^{\circ}\text{C}

. Spatial constraints limit the rod’s diameter to no more than

1.5\,\text{cm}

. Copper has thermal conductivity

400\,\text{W}\!/\!(\text{m}\cdot\!^{\circ}\text{C})

. Which statement correctly describes whether the design goal is achievable and, if not, what diameter would be required? a) No; the rod would need a diameter of roughly

3.6\,\text{cm}

to conduct the required power. b) Yes; the goal is achievable with the maximum allowed diameter of

1.5\,\text{cm}

. c) No; the rod would need a diameter of roughly

7.3\,\text{cm}

to conduct the required power. d) No; the rod would need a diameter of roughly

14.6\,\text{cm}

to conduct the required power.

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