Latent heat and phase change
A physical process in which a conversion among the basic states or phases of matter, i.e., solid, liquid, and gas takes place under the effect of a certain temperature and pressure is referred to as a phase change. Generally, the phase change of a substance occurs when heat transfer takes place between the substance and its surroundings. Based on the direction in which heat transfer takes place, different types of phase changes can occur.
Triple Point of Water
The branch of physics in which observer deals with temperature related properties is called thermodynamics.
Boiling Point of Water
Everyday examples of boiling is, boiling milk, heating water. One would have observed that when we heat water it goes through various stages and at one point bubbles show in water, and water keeps splashing with bubbles bursting, we in layman terms say that water is boiling.
Freezing Point of Water
In general, the freezing point of water is 0° Celsius, or 32° Fahrenheit. This is the temperature at which water will ordinarily change from its liquid state to its solid state (ice). However, there are certain conditions that can affect the freezing point of water. For example, a liquid may be supercooled or contain impurities so that it does not freeze at the ordinary freezing point.
![### Heat Exchange in Ice-Water Mixture
**Problem Statement:**
1.0 kg of ice from a freezer at -20 °C is added to a reservoir containing 2.0 kg of water at 80 °C. Assuming no heat loss to the surroundings, the mixture reaches thermal equilibrium. Given the specific heat capacities:
- Specific heat of water: 4186 J/(kg·K)
- Specific heat of ice: 2090 J/(kg·K)
- Latent heat of fusion for ice: 3.35 x 10^5 J/kg
We are required to solve for the following:
a) How much heat is required to increase the temperature of the ice to 0 °C?
b) How much heat is required to melt the ice to water at 0 °C?
c) What is the final temperature of the mixture?
### Solution:
#### a) Heat required to raise the temperature of ice from -20 °C to 0 °C:
The formula to calculate the heat (Q) required to change the temperature of a substance is:
\[ Q = m \cdot c \cdot \Delta T \]
Where \( m \) is the mass, \( c \) is the specific heat capacity, and \( \Delta T \) is the change in temperature.
For ice:
\[ m = 1.0 \, \text{kg} \]
\[ c = 2090 \, \text{J/(kg·K)} \]
\[ \Delta T = 0 \, °C - (-20 \, °C) = 20 \, °C \]
So,
\[ Q = 1.0 \, \text{kg} \times 2090 \, \text{J/(kg·K)} \times 20 \, \text{K} \]
\[ Q = 41800 \, \text{J} \]
#### b) Heat required to melt the ice to water at 0 °C:
The formula to calculate the heat (Q) required to melt a substance is:
\[ Q = m \cdot L_f \]
Where \( L_f \) is the latent heat of fusion.
For ice:
\[ m = 1.0 \, \text{kg} \]
\[ L_f = 3.35 \times 10^5 \, \text{J/kg} \]
So,
\[ Q](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fec99e2ce-f146-4dfd-8358-2828b726596b%2F0690372e-7a79-4825-92c6-12d8142157fd%2Fz043lig_processed.jpeg&w=3840&q=75)
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