A piece of ice, 100 g in mass is kept at 0°C. The amount of heat it requires to melt at 0°C is (take latent heat of melting of ice to be 333.6 J/g):
33360 J
Calculating the Heat Required to Melt Ice at 0°C
This question asks us to find the amount of heat energy needed to melt a specific mass of ice at its melting point. When a substance changes its state, like from solid ice to liquid water, it requires a certain amount of heat energy without changing its temperature. This energy is known as latent heat.
Understanding Latent Heat of Melting
The latent heat of melting (or fusion) is the amount of heat energy required to change a unit mass of a substance from its solid state to its liquid state at its melting point, under standard atmospheric pressure. For ice, the latent heat of melting is given as 333.6 J/g. This means that 333.6 Joules of heat energy are needed to melt just 1 gram of ice at 0°C into 1 gram of water at 0°C.
Applying the Formula to Find Heat Required
To calculate the total heat required to melt a given mass of ice, we use a simple formula:
Heat Required (\(Q\)) = Mass of Substance (\(m\)) \(\times\) Latent Heat of Melting (\(L\))
In this problem, we are given the following values:
- Mass of the ice (\(m\)) = 100 g
- Latent heat of melting of ice (\(L\)) = 333.6 J/g
Now, we can plug these values into the formula to find the total heat required (\(Q\)).
\( Q = m \times L \)
\( Q = 100 \text{ g} \times 333.6 \text{ J/g} \)
\( Q = 33360 \text{ J} \)
So, the amount of heat required to melt 100 g of ice at 0°C is 33360 Joules.
Summary of Calculation
| Quantity | Symbol | Value | Units |
|---|---|---|---|
| Mass of ice | m | 100 | g |
| Latent Heat of Melting | L | 333.6 | J/g |
| Heat Required | Q | \(100 \times 333.6\) = 33360 | J |
The calculation confirms that 33360 J of heat energy is necessary to change 100 g of ice at 0°C completely into water at 0°C.
Revision Table: Key Concepts in Heat Transfer
| Concept | Description | Formula |
|---|---|---|
| Specific Heat Capacity | Heat required to raise the temperature of 1 unit mass of a substance by 1 degree Celsius (or Kelvin). | \(Q = mc\Delta T\) |
| Latent Heat of Fusion (Melting) | Heat required to change 1 unit mass of a substance from solid to liquid at its melting point. | \(Q = mL_f\) |
| Latent Heat of Vaporization | Heat required to change 1 unit mass of a substance from liquid to gas at its boiling point. | \(Q = mL_v\) |
Additional Information on Phase Changes and Heat
Phase changes are physical processes where a substance changes from one state (solid, liquid, gas) to another due to the addition or removal of heat energy. These changes happen at constant temperatures specific to the substance (melting point, boiling point) under given pressure.
- Melting: Solid to liquid (requires heat, uses latent heat of fusion).
- Freezing: Liquid to solid (releases heat, equal to latent heat of fusion).
- Boiling/Vaporization: Liquid to gas (requires heat, uses latent heat of vaporization).
- Condensation: Gas to liquid (releases heat, equal to latent heat of vaporization).
- Sublimation: Solid directly to gas (requires heat).
- Deposition: Gas directly to solid (releases heat).
During a phase change, the energy supplied (latent heat) is used to break the intermolecular bonds holding the substance in its initial state, rather than increasing the kinetic energy of the molecules (which would increase temperature). Once the phase change is complete, any additional heat supplied will again increase the temperature of the substance, calculated using its specific heat capacity.
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