Question

Heat flows through a wooden board 30mm thick at 0.0086 W/cm² when one of its sides is 20°C warmer than the other. Determine the thermal conductivity of the wood.

A. 0.0029 W/(cm·°C)
B. 0.0086 W/(cm·°C)
C. 0.0172 W/(cm·°C)
D. 0.0043 W/(cm·°C)

Answer 1

The thermal conductivity of the wooden board is approximately 0.00129 W/(cm·°C).

Step-by-step explanation:

To determine the thermal conductivity of the wooden board, we need to use the formula for heat conduction:

Q = kA(delta T)/d

Where:

• Q = heat flow (in watts)
• k = thermal conductivity (in W/(cm·°C))
• A = area (in cm²)
• delta T = temperature difference (in °C)
• d = thickness (in cm)

From the question, we know that:

• delta T = 20°C
• A = 1 cm² (since the area is not specified, we assume a small area so that the value of Q will be in W)
• d = 30 mm = 3 cm
• Q = 0.0086 W/cm² (given)

Plugging in these values into the formula, we get:

0.0086 = k(1)(20)/3

k = 0.0086(3)/20 = 0.00129 W/(cm·°C)

Therefore, the thermal conductivity of the wood is approximately 0.00129 W/(cm·°C).