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100 grams of ice at 0°C is put in 240 grams of water at 5°C. The mixtu

June 1, 2025 by rawan239

100 grams of ice at 0°C is put in 240 grams of water at 5°C. The mixture finally comes to equilibrium at 0°C with m grams of ice melted in the process. Value of m is close to : (latent heat of ice = 3.33 × 10⁵ J/kg and specific heat of water = 4.2 J g^-1°C)

0 g

10 g

5 g

15 g

This question was previously asked in

UPSC Geoscientist – 2024

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When the ice at 0°C is put into water at 5°C, the water will lose heat as it cools down to 0°C. This heat is then used to melt the ice at 0°C.

The heat lost by the water is Q_water = m_water * c_water * ΔT_water. Given m_water = 240 g, c_water = 4.2 J g⁻¹°C⁻¹, and ΔT_water = 5°C – 0°C = 5°C. Q_water = (240 g) * (4.2 J g⁻¹°C⁻¹) * (5°C) = 5040 J. This heat melts a mass m of ice. The heat required to melt ice is Q_melt = m * L_f. Given L_f = 3.33 × 10⁵ J/kg = 3.33 × 10⁵ J / 1000 g = 333 J/g.

Setting the heat lost by water equal to the heat gained by the melting ice: 5040 J = m (g) * 333 J/g. m = 5040 / 333 g ≈ 15.135 g. The value of m is closest to 15 g among the given options.

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