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A cooking vessel on a slow burner contains 5 kg of water and an unknown mass of ice in equilibrium at 0 o C at time t = 0. The temperature of the mixture is measured at various times and the result is plotted as shown in diagram. During the first 50 min the mixture remains at 0 o C. From 50 min to 60 min, the temperature increases to 2 o C. Neglecting the heat capacity of the heat capacity of the vessel, the initial

Options

  1. A1 0 7 kg
  2. B5 7 kg
  3. C5 4 kg
  4. D5 8 kg

Correct answer

B. 5 7 kg

Step-by-step solution

Let m be the mass of ice. Rate of heat given by the burner is constant. In the first 50 min dQ dt = mL t 1 = m kg × 8 0 × 4.2 × 1 0 3 J/kg 5 0 min ...(i) From 50 min to 60 min dQ dt = m + 5 S H 2 O Δ θ t 2 = m + 5 4.2 × 1 0 3 J/kg × 2 ∘ C 1 min ...(ii) From Eqs. (i) and (ii) 8 0 m 5 0 = 2 m + 5 1 0 7 m = 5 ⇒ m = 5 7 kg ≃ 0.7 kg

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