A cubic container full of hot water at a temperature of 90 °C is completely lagged with an insulating material of thermal conductivity 6.4x10-4 Wcm-1K-1 (6.4x10-2 Wm-1K-1). The edges of the container are 1.0 m long and the thickness of the lagging is 1.0 cm. Estimate the rate of flow of heat through the lagging if the external temperature of the lagging is 40 °C.

Question

A cubic container full of hot water at a temperature of 90 °C is completely lagged with an insulating material of thermal conductivity 6.4x10-4 Wcm-1K-1 (6.4x10-2 Wm-1K-1). The edges of the container are 1.0 m long and the thickness of the lagging is 1.0 cm. Estimate the rate of flow of heat through the lagging if the external temperature of the lagging is 40 °C.

Answer 1

To estimate the rate of flow of heat through the lagging, we can use Fourier's Law of Heat Conduction:

Q = (k * A * ΔT) / L

Where:
Q is the rate of flow of heat,
k is the thermal conductivity of the lagging material,
A is the surface area of the container,
ΔT is the temperature difference between the hot water and the external temperature,
L is the thickness of the lagging.

First, let's convert the thermal conductivity from Wm-1K-1 to Wcm-1K-1:
k = 6.4x10-2 Wm-1K-1 = 6.4x10-2 * (1/100) Wcm-1K-1 = 6.4x10-4 Wcm-1K-1

The surface area of the container can be calculated by multiplying the length of one side by itself and then multiplied by six (since there are six faces of a cube):
A = (1.0 m * 1.0 m) * 6 = 6.0 m^2

Now we can plug in the values into the equation:

Q = (6.4x10-4 Wcm-1K-1 * 6.0 m^2 * (90 °C - 40 °C)) / (1.0 cm)

Simplifying the equation:

Q = (6.4x10-4 * 6.0 * (90 - 40)) / 1.0 W

Calculating the rate of flow of heat through the lagging:

Q = 6.4x10-4 * 6.0 * 50 W
Q ≈ 0.0192 W

Therefore, the estimated rate of flow of heat through the lagging is approximately 0.0192 W.

Answer 2

To estimate the rate of flow of heat through the lagging, you can use Fourier's Law of Heat Conduction. Fourier's Law states that the rate of flow of heat (Q) is equal to the product of thermal conductivity (k), temperature difference (ΔT), and surface area (A), divided by the thickness (L).

Mathematically, it can be expressed as:
Q = (k * A * ΔT) / L

In this case, we are given:
- Thermal conductivity (k) = 6.4x10-2 Wm-1K-1
- Temperature difference (ΔT) = 90 °C - 40 °C = 50 °C
- Surface area (A) = 6 faces of a cube = 6 * (1.0 m * 1.0 m) = 6 m^2
- Thickness (L) = 1.0 cm = 0.01 m

Substituting the given values into Fourier's Law equation, we get:
Q = (6.4x10-2 Wm-1K-1 * 6 m^2 * 50 °C) / 0.01 m

Calculating the value, we have:
Q = (6.4 * 6 * 50) W = 1920 W

Therefore, the estimated rate of flow of heat through the lagging is 1920 Watts.

Good

None

To estimate the rate of flow of heat through the lagging, we can use Fourier's Law of Heat Conduction:

To estimate the rate of flow of heat through the lagging, you can use Fourier's Law of Heat Conduction. Fourier's Law states that the rate of flow of heat (Q) is equal to the product of thermal conductivity (k), temperature difference (ΔT), and surface area (A), divided by the thickness (L).