Two metal rods,one silver and the other copper,are both immersed at one end in a steam chamber at a temperature of 100°C.The other end of each one is in an ice water bath at 0°C.The rods are 5.0 cm long and have a square cross-section that is 2.0 cm on a side.No heat is exchanged between the rods and the surroundings,except at the ends.How much total heat flows through the two rods each minute? The thermal conductivity of silver is 417 W/m ∙ K,and that of copper is 395 W/m ∙ K.

Question

Quizplus · Accepted Answer

First, we need to find the heat transferred through each rod using the formula: 
$q = \frac{kA\Delta T}{L}$ 
where 
$q$ = heat transferred 
$k$ = thermal conductivity 
$A$ = cross-sectional area 
$\Delta T$ = temperature difference 
$L$ = length

For the silver rod: 
$q_{silver} = \frac{(417\ W/m \cdot K) \cdot (2.0 \ cm)^2 \cdot (100 - 0) \ K}{5.0 \ cm} = 166.8\ J/s$

For the copper rod: 
$q_{copper} = \frac{(395\ W/m \cdot K) \cdot (2.0 \ cm)^2 \cdot (100 - 0) \ K}{5.0 \ cm} = 157.6\ J/s$

Now, we can find the total heat transferred each minute: 
$Q_{total} = (q_{silver} + q_{copper}) \cdot 60\ s = (166.8 + 157.6) \ J/s \cdot 60\ s = 20040\ J = 20.04\ kJ \approx \boxed{	extbf{(B)}\ 39\ kJ}$

Two Metal Rods,one Silver and the Other Copper,are Both Immersed