A solid of mass 0.5kg initially at 50oC melts at 60oC. Calculate the quantity of heat required to melt it…

Analyze the question: The solid starts at 50°C and must first be heated to its melting point (60°C). Then it melts completely at constant temperature. So the total heat has two parts:

1. Heat to raise the temperature: Q₁ = mcΔθ
2. Heat to melt it: Q₂ = mL

Concept: Total heat = heat for warming + heat for change of state (the temperature stays constant during melting).

Solution:

Given: m = 0.5 kg, c = 2.0 kJ kg⁻¹K⁻¹ = 2000 J kg⁻¹K⁻¹, L = 1.0 kJ kg⁻¹ = 1000 J kg⁻¹, Δθ = 60 − 50 = 10 K

Step 1: Q₁ = 0.5 × 2000 × 10 = 10,000 J

Step 2: Q₂ = mL = 0.5 × 1000 = 500 J

Step 3: Total Q = 10,000 + 500 = 10,500 J

Answer: C. 10500 J.

Tip: When a question gives an initial temperature below the melting point, always add the heating stage (mcΔθ) to the latent heat stage (mL). Also convert kJ to J before calculating. Forgetting either step leads to the wrong options (B = heating only, A = a common slip).