To calculate the work needed to evaporate water from washed clothes in a well-isolated room at 75°F, the energy required can be determined using the formula Q = m h_{fg}, where Q is the energy, m is the mass of water, and h_{fg} is the latent heat of vaporization. Additionally, the sensible heat must be considered, incorporating the specific heat and temperature change with the equation q = m h_{fg} + m c_{p} ΔT. This approach highlights that the energy required for evaporation varies with the initial temperature of the water. The discussion also emphasizes the importance of calculating the energy costs associated with line drying versus using an electric dryer, factoring in the energy needed to maintain the room temperature. Understanding these calculations can help in estimating potential savings from line drying clothes.