Specific Latent Heat

Specific latent heat of fusion is the amount of heat required to change a unit mass of solid substance into liquid at constant temperature.

0.6 kg of ice at -10°C is dropped into 2 kg of water at 49°C, contained in a copper calorimeter of mass 0.15 kg. If the final temperature of the mixture is 20°C, find the specific latent heat of fusion of ice.

Given:

• Mass of ice, $M_{ice} = 0.6 \, \text{kg}$
• Initial temperature of ice = -10°C
• Final temperature of mixture = 20°C
• Mass of water, $M_{water} = 2 \, \text{kg}$
• Initial temperature of water = 49°C
• Mass of calorimeter, $M_{cal} = 0.15 \, \text{kg}$
• Specific heat capacity of ice = $2.1 \times 10^3 \, \text{J/kg°C}$
• Specific heat capacity of water = $4.2 \times 10^3 \, \text{J/kg°C}$
• Specific heat capacity of copper = $420 \, \text{J/kg°C}$

Step 1: Heat gained by ice warming from -10°C to 0°C

$Q_1 = 0.6 \times 2.1 \times 10^3 \times 10 = 12600 \, \text{J}$

Step 2: Heat gained by ice during melting at 0°C

$Q_2 = 0.6L \quad (\text{where } L \text{ is latent heat of fusion})$

Step 3: Heat gained by melted ice (now water) warming from 0°C to 20°C

$Q_3 = 0.6 \times 4.2 \times 10^3 \times 20 = 50400 \, \text{J}$

Step 4: Heat lost by water cooling from 49°C to 20°C

$Q_4 = 2 \times 4.2 \times 10^3 \times (49 - 20) = 2 \times 4.2 \times 10^3 \times 29 = 243600 \, \text{J}$

Step 5: Heat lost by copper calorimeter cooling from 49°C to 20°C

$Q_5 = 0.15 \times 420 \times 29 = 1827 \, \text{J}$

Total heat gained = total heat lost

$12600 + 0.6L + 50400 = 243600 + 1827$

$63000 + 0.6L = 245427$

$0.6L = 245427 - 63000 = 182427$

$L = \frac{182427}{0.6} = 304045 \, \text{J/kg}$

So, the specific latent heat of fusion of ice is 304045 J/kg.

A refrigerator is a machine that enables heat to flow from a cold region to a hot region. The basic principle it uses is cooling by absorption of latent heat.

How it works:

1. A volatile liquid (e.g. Freon) evaporates inside copper coils surrounding the freezing compartment of the refrigerator.
2. The latent heat of vaporisation is absorbed from the surroundings (inside the freezer), which causes the air inside to cool.
3. An electric pump removes the vapor from the evaporator coils and compresses it into a heat exchanger.
4. In the heat exchanger, the vapor is condensed back into liquid, releasing the absorbed latent heat to the surrounding air through fins attached to the coils.
5. The liquid Freon is returned to the evaporator coils through a valve, continuing the cycle.
6. A thermostat controls the rate of evaporation and maintains the desired low temperature by switching the pump on and off automatically.