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What is the thermal conductivity of a material if a 1 m² area of it conducts 100

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Question: What is the thermal conductivity of a material if a 1 m² area of it conducts 100 J of heat in 10 seconds with a temperature difference of 20°C?

Options:

  1. 2 W/m°C
  2. 5 W/m°C
  3. 10 W/m°C
  4. 20 W/m°C

Correct Answer: 5 W/m°C

Solution: 

Using the formula Q = kA(T1-T2)t, we find k = Q / (A(T1-T2)t) = 100 J / (1 m² * 20°C * 10 s) = 0.5 W/m°C.

What is the thermal conductivity of a material if a 1 m² area of it conducts 100

Practice Questions

Q1
What is the thermal conductivity of a material if a 1 m² area of it conducts 100 J of heat in 10 seconds with a temperature difference of 20°C?
  1. 2 W/m°C
  2. 5 W/m°C
  3. 10 W/m°C
  4. 20 W/m°C

Questions & Step-by-Step Solutions

What is the thermal conductivity of a material if a 1 m² area of it conducts 100 J of heat in 10 seconds with a temperature difference of 20°C?
  • Step 1: Identify the given values from the question. We have Q (heat conducted) = 100 J, A (area) = 1 m², (T1 - T2) (temperature difference) = 20°C, and t (time) = 10 seconds.
  • Step 2: Write down the formula for thermal conductivity: Q = k * A * (T1 - T2) * t.
  • Step 3: Rearrange the formula to solve for k (thermal conductivity): k = Q / (A * (T1 - T2) * t).
  • Step 4: Substitute the known values into the rearranged formula: k = 100 J / (1 m² * 20°C * 10 s).
  • Step 5: Calculate the denominator: 1 m² * 20°C * 10 s = 200 m²°C·s.
  • Step 6: Now divide the heat conducted (100 J) by the calculated denominator (200 m²°C·s): k = 100 J / 200 m²°C·s.
  • Step 7: Perform the division: k = 0.5 W/m°C.
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