To find the latent heat of fusion of the final solution when two liquids with different latent heat of fusion are mixed together, you can use a weighted average approach. Here's how you can calculate it:
Determine the latent heat of fusion (L1) for the first liquid, which is water in this case. The latent heat of fusion for water is approximately 334,000 J/kg.
Determine the latent heat of fusion (L2) for the second liquid, which is sucrose in this case. The latent heat of fusion for sucrose is approximately 346,000 J/kg.
Calculate the weighted average latent heat of fusion (Lf) for the final solution using the proportions of the two liquids. In this case, you have an 80% water and 20% sucrose solution.
Lf = (0.8 * L1) + (0.2 * L2)
Lf = (0.8 * 334,000 J/kg) + (0.2 * 346,000 J/kg)
Lf = 267,200 J/kg + 69,200 J/kg
Lf ≈ 336,400 J/kg
Therefore, the approximate latent heat of fusion for the final solution, which is a mixture of 80% water and 20% sucrose, is approximately 336,400 J/kg.
Keep in mind that the values used here are approximate and may vary depending on the specific conditions and properties of the liquids.