Exactly 6.975 grams of ice can be melted by 558 cal of energy.
Understanding the Melting Process
When ice melts, the absorbed energy does not increase its temperature; instead, it changes its physical state from solid to liquid. This specific amount of energy required for a phase change at a constant temperature is known as the latent heat. For melting (solid to liquid), it's called the latent heat of fusion.
The latent heat of fusion of ice is a crucial physical constant that quantifies how much energy is needed to transform a certain mass of ice into water at 0°C (32°F). This energy breaks the bonds holding the water molecules in their rigid crystalline structure as ice, allowing them to move freely as liquid water.
Key Principle: Latent Heat of Fusion
The amount of energy required to melt a substance is directly proportional to its mass and its specific latent heat of fusion. For ice, the accepted value for the latent heat of fusion ($L_f$) is approximately 80 calories per gram (cal/g) or 334 Joules per gram (J/g). This means that 80 calories of energy are needed to melt just one gram of ice.
Calculating the Mass of Melted Ice
To determine the mass of ice that can be melted by a given amount of energy, we use the following formula:
$Q = m \times L_f$
Where:
- $Q$ is the total heat energy supplied (in calories).
- $m$ is the mass of the substance melted (in grams).
- $L_f$ is the latent heat of fusion (in calories per gram).
We can rearrange this formula to solve for the mass ($m$):
$m = \frac{Q}{L_f}$
Given Values:
- Energy ($Q$) = 558 cal
- Latent Heat of Fusion of Ice ($L_f$) = 80 cal/g
Calculation:
| Variable | Value | Unit |
|---|---|---|
| Energy (Q) | 558 | cal |
| Latent Heat of Fusion (Lf) | 80 | cal/g |
| Mass of Ice (m) | ? | g |
$m = \frac{558 \text{ cal}}{80 \text{ cal/g}}$
$m = 6.975 \text{ g}$
Therefore, 558 calories of energy can melt exactly 6.975 grams of ice.
Practical Applications
Understanding the latent heat of fusion has various practical applications, from everyday phenomena to industrial processes:
- Cooling Beverages: Ice is highly effective at cooling drinks because it absorbs a large amount of heat energy (its latent heat of fusion) as it melts, without raising its own temperature. This keeps the beverage at 0°C until all the ice has melted.
- Cold Packs: Chemical cold packs often use endothermic reactions that absorb heat from their surroundings, mimicking the effect of melting ice to provide cooling.
- Meteorology and Climate: The melting of ice caps and glaciers is a critical process influenced by the absorption of large quantities of solar energy, playing a significant role in global climate systems and sea-level rise.
- Food Preservation: Ice is used to preserve food by keeping it at a low temperature, which slows down spoilage. The large amount of energy absorbed during melting makes it an efficient cooling agent for extended periods.
This calculation demonstrates a fundamental principle of thermodynamics, highlighting how energy interacts with matter during phase transitions.
