This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
To determine the quantity of water evaporated, we need to calculate the total heat transferred through the aluminum pan and then use the latent heat of vaporization. Given values: • Thickness of aluminum pan (L) = 15 mm = 15 × 10^-3 m = 0.015 m • Heating surface area (A) = 2.5 mm^2 = 2.5 × (10^-3 m)^2 = 2.5 × 10^-6 m^2 • Temperature difference ( T) = 75^ = 75 K • Time (t) = 5 minutes = 5 × 60 s = 300 s • Thermal conductivity of aluminum (K_Al) = 237 Wm^-1K^-1 • Latent heat of vaporization of water (L_w) = 2.2 × 10^6 Jkg^-1 (assuming the unit JK^-1 in the question is a typo and should be Jkg^-1) Step 1: Calculate the rate of heat transfer (Q_rate) through the aluminum pan using the formula for conduction. Q_rate = K_Al A TL Q_rate = 237 Wm^-1K^-1 × 2.5 × 10^-6 m^2 × 75 K0.015 m Q_rate = 44437.5 × 10^-60.015 W Q_rate = 2.9625 W Step 2: Calculate the total heat transferred (Q_total) in 5 minutes. Q_total = Q_rate × t Q_total = 2.9625 W × 300 s Q_total = 888.75 J Step 3: Calculate the mass of water evaporated (m) using the total heat transferred and the latent heat of vaporization. Q_total = m × L_w m = Q_totalL_w m = 888.75 J2.2 × 10^6 Jkg^-1 m = 403.977... × 10^-6 kg m ≈ 0.000404 kg Rounding to four decimal places, the mass of water evaporated is approximately 0.0004 kg. The final answer is A. 0.0004Kg. Last free one today — make it count tomorrow, or type /upgrade for unlimited.