Two metal rods,one silver and the other copper,are both attached to a steam chamber as shown in the figure,with a temperature of 100°C,at one end,and an ice water bath,with a temperature of 0°C,at the other.The rods are 5.0 cm long and have a square cross-section, on a side.When steady state has been reached,how much heat flows through the two rods in 1.0 min? The thermal conductivity of silver is ,and that of copper is .No heat is exchanged between the rods and the surroundings,except at their ends.

Question

Two metal rods,one silver and the other copper,are both attached to a steam chamber as shown in the figure,with a temperature of 100°C,at one end,and an ice water bath,with a temperature of 0°C,at the other.The rods are 5.0 cm long and have a square cross-section,  on a side.When steady state has been reached,how much heat flows through the two rods in 1.0 min? The thermal conductivity of silver is  ,and that of copper is  .No heat is exchanged between the rods and the surroundings,except at their ends.

Quizplus · Accepted Answer

The heat flow through each rod can be calculated using the formula:

Q = kA∆T/t

where Q is the heat flow, k is the thermal conductivity, A is the cross-sectional area, ∆T is the temperature difference between the ends, and t is the time.

For the silver rod:

Q_silver = (11.7 J/(s·m·K)) * (0.11 m)^2 * (100°C - 0°C) / (60 s)

Q_silver = 48.2 J/s = 2.89 kJ/min

For the copper rod:

Q_copper = (401 J/(s·m·K)) * (0.11 m)^2 * (100°C - 0°C) / (60 s)

Q_copper = 163 J/s = 9.77 kJ/min

The total heat flow is the sum of the heat flows through each rod:

Q_total = Q_silver + Q_copper = 2.89 kJ/min + 9.77 kJ/min

Q_total = 12.66 kJ/min ≈ 39 kJ (rounded to two significant figures)

Therefore, the best choice is B, which gives the closest value to our calculation.

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