What is the amount of heat required to raise the temperature of a 0.02 kg of ice cube from -10°C to

What is the amount of heat required to raise the temperature of a 0.02 kg of ice cube from -10°C to 10°C? [specific latent heat of fusion of ice = 3.34 x 10⁵ Jkg^-1, Specific heat capacity of water = 4200 Jkg^-1K^-1, Specific heat capacity of ice = 2100 Jkg^-1K^-1]

Explanation

Step 1: Identify given values and what to find
Given: m = 0.02 kg, T₁ = -10°C, T₂ = 10°C, L_f = 3.34 × 10⁵ Jkg⁻¹, c_ice = 2100 Jkg⁻¹K⁻¹, c_water = 4200 Jkg⁻¹K⁻¹
Find: Total heat Q

Step 2: Heat ice from -10°C to 0°C
Formula: Q₁ = mc_ice ΔT
Q₁ = 0.02 × 2100 × 10 = 420 J

Step 3: Melt ice at 0°C
Formula: Q₂ = mL_f
Q₂ = 0.02 × 3.34 × 10⁵ = 6680 J

Step 4: Heat water from 0°C to 10°C
Formula: Q₃ = mc_water ΔT
Q₃ = 0.02 × 4200 × 10 = 840 J

Step 5: Calculate total heat
Total Q = Q₁ + Q₂ + Q₃ = 420 + 6680 + 840 = 7940 J

Step 6: The answer is 7940 J