The quantity of heat energy required to melt completely 1 kg of ice at - 30oC is [latent heat of fusion = 3.5…

Analyze the question: Ice at -30°C must first be warmed to 0°C, and then melted at 0°C. So there are two heat stages.

Concept:

• Heating without a change of state: Q₁ = mcΔθ
• Melting at constant temperature: Q₂ = mL

Solution:

Stage 1: warm the ice from -30°C to 0°C Q₁ = mcΔθ = 1 × 2.1×10³ × 30 = 6.3×10⁴ J

Stage 2: melt the ice at 0°C Q₂ = mL = 1 × 3.5×10⁵ = 3.5×10⁵ J

Total heat: Q = Q₁ + Q₂ = 0.63×10⁵ + 3.5×10⁵ = 4.13×10⁵ J

Tip: When ice starts below 0°C, always add the "warming" step (mcΔθ) before the "melting" step (mL). Many students forget the first step and pick 3.5×10⁵ J. Also watch the powers of 10: 6.3×10⁴ must be converted to 0.63×10⁵ before adding to 3.5×10⁵.