Question

A pupil adds 37g of ice at 0°C to 100g of water at 30°C. The final temperature of the water and melted ice is 0°C. no heat is lost to, or gained from, the surroundings.

The specific heat capacity of water is 4.2 J/ (g°C)
what is the specific latent heat of ice?
A) 47 J/g c) 4700 J/g
b) 341 J/g d) 12600 J/g

Answer 1

The specific latent heat of ice is approximately 341 J/g

The correct option is;

b) 341 J/g

Step-by-step explanation:

The given parameters are;

The mass of ice the pupil adds to the water, m₁ = 37 g

The initial temperature of the ice, T₁ = 0°C

The mass of the water to which the ice is added, m₂ = 100 g

The initial temperature of the water, T₂₁ = 30°C

The final temperature of the water and the melted ice, T₂₂ = 0°C

The specific heat capacity of the water, c₂ = 4.2 J/(g·°C)

By the principle of conservation of energy, we have;

The heat gained by the ice = The heat lost by the water = ΔQ₂

Given that the ice is only melted with no change in temperature, we have;

The heat gained by the ice = The latent heat needed for melting the ice

ΔQ₂ = m₂ × c₂ × (T₂₂ - T₂₁) = 100 × 4.2 × (0 - 30) = -12,600 J

The heat gained by the ice = m₁ ×
`L_f`

Where;

`L_f` represents the specific latent heat of fusion of ice;

We have;

12,600 = 37 ×
`L_f`

`L_f` = 12,600/37 = 340.54 J/g ≈ 341 J/g

The specific latent heat of fusion of ice =
`L_f` ≈ 341 J/g.