Question

How much heat is required to increase the temperature of 85.44 g of water from −18.6 °C to 33.4 °C?

NOTE

H₂O (s) → H₂O (l) ΔH°_{fusion, water} = 6.02 kJ/mol

Specific Heat Capacities:

c_{water (l)} = 4.186 J·g^-1·°C^-1

c_{water (s)} = 2.056 J·g^-1·°C^-1

Answer 1

We require 2 type of heat, latent heat and sensible heat

Sensible heat (CP): heat change due to Temperature difference

Latent heat (LH): Heat involved in changing phases (no change of T)

Then

Q1 = m*Cp ice * (Tf – T1)

Q2 = m*LH ice

Q3 = m*Cp wáter * (Tb – Tf)

Note that Tf = 0°C; Tb = 100°C, LH ice = 334 kJ/kg; LH water = 2264.76 kJ/kg.

Cp ice = 2.01 J/g°C ; Cp water = 4.184 J/g°C; Cp vapor = 2.030 kJ/kg°C

Then

Q1 = 85.44*2.01 * (0 – -18)

Q2 = 85.44*334

Q3 = 85.44*4.184 * (33.4– 0)

Qt = 3091.2192 + 28536.96 + 11939.864064

Qt = 43568.04J

Qt = 43.568 kJ