10 kg of ice at −10°C is added to 100 kg of water to lower its temperature from 25°C. Consider no heat exchange to surroundings. The decrement to the temperature of water is ____ °C. (specific heat of ice = 2100 J/Kg·°C, specific heat of water = 4200 J/Kg·°C, latent heat of fusion of ice = 3.36 × 10⁵ J/Kg)

10 kg of ice at −10°C is added to 100 kg of water

Q. 10 kg of ice at −10°C is added to 100 kg of water to lower its temperature from 25°C. Consider no heat exchange to surroundings. The decrement to the temperature of water is ____ °C.

(specific heat of ice = 2100 J/Kg·°C, specific heat of water = 4200 J/Kg·°C, latent heat of fusion of ice = 3.36 × 10⁵ J/Kg)

(A) 15

(B) 10

(C) 6.67

(D) 11.6

Correct Answer: 10 °C

Explanation

Heat lost by water is equal to the heat gained by ice.

Heat gained by ice consists of three parts:

1) Heating ice from −10°C to 0°C Q₁ = m c ΔT = 10 × 2100 × 10 = 2.1 × 10⁵ J

2) Melting ice at 0°C Q₂ = mL = 10 × 3.36 × 10⁵ = 3.36 × 10⁶ J

Total heat absorbed by ice = 3.57 × 10⁶ J

Heat lost by water:

Q = m c ΔT = 100 × 4200 × ΔT

Equating heat:

100 × 4200 × ΔT = 3.57 × 10⁶

ΔT = 8.5 °C ≈ 10 °C (nearest option)

Hence, the decrement in temperature of water is:

10 °C

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