Heat of Fusion and heat of vaporization

Heat of fusion and heat of vaporization

Sample problem:

How many calories of heat are required by 100grams of ice at -5⁰C to change to steam at 120⁰C?

1. Heat to raise temperature of ice to 0⁰C, the melting point (Q₁)?

Given:

m = 100g t₂ = 0

S_ice = 0.5 cal/g ⁰C t₁ = - 5⁰C

Find Q₁

Formula Q₁ = m s Δt

Substitution: Q₁ = (100g) (0.5 cal/g ⁰C) [0 – (- 5⁰C)]

Answer: Q₁ = 250 cal

2. Heat to melt ice at O⁰C (Q₂)?

Given:

m = 100g h_f = 80 cal/g

Find Q₂

Formula Q₂ = m h_f

Substitution: Q₂ = (100g) (80 cal/g)

Answer: Q₂ = 8000 cal

3. Heat to raise the temperature of water at 0⁰C to 100⁰C (Q₃)?

Given:

m = 100g t₂ = 100⁰C

S_water = 1 cal/g ⁰C t₁ = 0

Find Q₃

Formula Q₃ = m s Δt

Substitution: Q₃ = (100g) (1 cal/g ⁰C) (100⁰C-0)

Answer: Q₃ = 10,000 cal

4. Heat to convert water at 100⁰C (Q₄)?

Given:

m = 100g h_v = 540 cal/g

Find Q₄

Formula Q₄ = m h_v

Substitution: Q₄ = (100g) (540 cal/g )

Answer: Q₄ = 54,000 cal

5. Heat to raise the temperature of steam at 100⁰C to 120⁰C (Q₅)?

Given:

m = 100g t₂ = 120⁰C

S_steam = 0.48 cal/g ⁰C t₁ = 100⁰C

Find Q₅

Formula Q₅ = m s Δt

Substitution: Q₅ = (100g) (0.48 cal/g ⁰C) (120⁰C- 100⁰C)

Answer: Q₅ = 960 cal

Q_T = Q₁ + Q₂ + Q₃ + Q₄ + Q₅

Q_T = 250 cal + 8,000 cal + 10,000 cal + 54,000 cal + 960 cal

Q_T = 73,210 cal

Practice problem:

1. How many calories of heat are required by 300grams of ice at -15⁰C to change to steam at 120⁰C?

2. How many calories of heat are required by 250grams of ice at -33⁰C to change to steam at 120⁰C?