Calculate the quantity of water evaporated from an aluminum pan with given dimensions, temperature difference, and time, using thermal conductivity and latent heat of vaporization.

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 ($L$) = $15 \text{ mm} = 15 \times 10^{-3} \text{ m} = 0.015 \text{ m}$
• Heating surface area ($A$) = $2.5 \text{ mm}^2 = 2.5 \times (10^{-3} \text{ m})^2 = 2.5 \times 10^{-6} \text{ m}^2$
• Temperature difference ($\Delta T$) = $75^\circ\text{C} = 75 \text{ K}$
• Time ($t$) = $5 \text{ minutes} = 5 \times 60 \text{ s} = 300 \text{ s}$
• Thermal conductivity of aluminum ($K_{Al}$) = $237 \text{ Wm}^{-1}\text{K}^{-1}$
• Latent heat of vaporization of water ($L_w$) = $2.2 \times 10^6 \text{ Jkg}^{-1}$ (assuming the unit $\text{JK}^{-1}$ in the question is a typo and should be $\text{Jkg}^{-1}$)