Question

The thermal conductivity of aluminum is 238 J/s·m·°C and of copper is 397 J/s·m·°C. A rod of each material is used as a heat conductor.

If the rods have the same geometry and are used between the same temperature differences for the same time interval, what is the ratio of the heat transferred by the aluminum to the heat transferred by the copper?
a. 0.599
b. 1.67
c. 0.359
d. 2.78

Answer 1

a. 0.599

Step-by-step explanation:

`k_(al)` = Thermal conductivity of aluminum = 238 J/(s·m·°C)

`k_(cu)` = Thermal conductivity of copper = 397 J/(s·m·°C)

`A` = Area of each rod

`d` = thickness of each rod

`\DeltaT` = Difference in temperature for each rod

`t` = time interval of use for each rod

Heat transferred by aluminum rod is given as

`Q_(al) = (k_(al) A\Delta T t)/(d)`

Heat transferred by copper rod is given as

`Q_(cu) = (k_(cu) A\Delta T t)/(d)`

Ratio of the heat transferred is given as

`Ratio = (Q_(al))/(Q_(cu)) = ((k_(al) A\Delta T t)/(d))/((k_(cu) A\Delta T t)/(d)) = (k_(al))/(k_(cu)) = (238)/(397) = 0.599`