To find the surface area of the vessel, we use the formula for the rate of heat transfer by conduction:

Question

ScanSolve AI Tutor · Accepted Answer

To find the surface area of the vessel, we use the formula for the rate of heat transfer by conduction:

Q = K A \frac{dT}{dx}

where:

Given values:

Calculate the rate of heat transfer ( $Q$ ).
The rate of heat transfer is the heat energy given off per second.
$Q = \frac{\text{Heat energy}}{\text{Time}} = \frac{1.2 \times 10^6 \text{ J}}{1 \text{ s}} = 1.2 \times 10^6 \text{ W}$
Rearrange the formula to solve for the surface area ( $A$ ).
$A = \frac{Q}{K \frac{dT}{dx}}$
Substitute the given values into the rearranged formula.
$A = \frac{1.2 \times 10^6 \text{ W}}{400 \text{ Wm}^{-1}\text{K}^{-1} \times 30 \text{ Km}^{-1}}$
Calculate the surface area.
$A = \frac{1.2 \times 10^6}{12000}$ $A = \frac{1.2 \times 10^6}{1.2 \times 10^4}$ $A = 10^{6-4}$ $A = 10^2 \text{ m}^2$
The surface area of the vessel is $1.0 \times 10^2 \text{ m}^2$ .

The final answer is $\text{A. } 1.0 \times 10^2 \text{m}^2$ .

Answer