When ‘m’ g of ice is added to ‘M’ g of water at 20 °C, state

1.	When ‘m’ g of ice is added to ‘M’ g of water at 20 °C, state the conditions for m and M for whichi) temperature of the mixture remains 0° C.ii) temperature of the mixture exceeds 0 °C.(Specific heat of water = sw = 4.2 × 103 J kg-1 °C-1, latent heat of fusion = L = 3.36 × 105 J kg-1)
Answer» The heat lost by water in going from 20 °C to 0°C, Q₁ = Ms_w ∆T = \(\frac{M}{1000}\) × 4.2 × 10³ × (20) = 84M J Now, heat required to convert m g of ice into water at 0 °C, Q₂ = mL = \(\frac{M}{1000}\) × 3.36 × 10⁵ = 336m J 1. For temperature of mixture to be 0 °C, Q₂ > Q₁ ⇒ 336m > 84M ⇒ m > \(\frac{M}{4}\) 2. For temperature of mixture to exceed 0 °C, Q₂ < Q₁ ⇒ m < \(\frac{M}{4}\)

When ‘m’ g of ice is added to ‘M’ g of water at 20 °C, state the conditions for m and M for whichi) temperature of the mixture remains 0° C.ii) temperature of the mixture exceeds 0 °C.(Specific heat of water = sw = 4.2 × 103 J kg-1 °C-1, latent heat of fusion = L = 3.36 × 105 J kg-1)

Answer»

The heat lost by water in going from 20 °C to 0°C,

Q₁ = Ms_w ∆T = \(\frac{M}{1000}\) × 4.2 × 10³ × (20) = 84M J

Now, heat required to convert m g of ice into water at 0 °C,

Q₂ = mL = \(\frac{M}{1000}\) × 3.36 × 10⁵ = 336m J

1. For temperature of mixture to be 0 °C,

Q₂ > Q₁

⇒ 336m > 84M

⇒ m > \(\frac{M}{4}\)

2. For temperature of mixture to exceed 0 °C,

Q₂ < Q₁ ⇒ m < \(\frac{M}{4}\)