This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
To find the surface area of the vessel, we use the formula for the rate of heat transfer by conduction: Q = K A (dT)/(dx) where: • Q is the rate of heat transfer (heat energy per unit time) • K is the thermal conductivity • A is the surface area • (dT)/(dx) is the temperature gradient Given values: • Heat energy given off = 1.2 × 10^6 J • Time = 1 s • Thermal Conductivity (K) = 400 Wm^-1K^-1 • Temperature gradient ((dT)/(dx)) = 30 Km^-1 Step 1: Calculate the rate of heat transfer (Q). The rate of heat transfer is the heat energy given off per second. Q = Heat energyTime = 1.2 × 10^6 J1 s = 1.2 × 10^6 W Step 2: Rearrange the formula to solve for the surface area (A). A = (Q)/(K dT)dx Step 3: Substitute the given values into the rearranged formula. A = 1.2 × 10^6 W400 Wm^-1K^-1 × 30 Km^-1 Step 4: Calculate the surface area. A = (1.2 × 10^6)/(12000) A = (1.2 × 10^6)/(1.2 × 10^4) A = 10^6-4 A = 10^2 m^2 The surface area of the vessel is 1.0 × 10^2 m^2. The final answer is A. 1.0 × 10^2 m^2. 3 done, 2 left today. You're making progress.