13) A Zookeeper puts eight ice blocks, each of mass 2.5 kg and temperature T= −15° C, in the penguin exhibit's pool of water which contains 100 L of water at T= 25° C. Assume a closed isolated system. (a) Does all of the ice melt? (b) What is the final temperature of the pool of water?
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.
![### Problem Statement
A zookeeper puts eight ice blocks, each of mass 2.5 kg and temperature \( T = -15^\circ \text{C} \), in the penguin exhibit’s pool of water which contains 100 L of water at \( T = 25^\circ \text{C} \). Assume a closed isolated system.
1. **Does all of the ice melt?**
2. **What is the final temperature of the pool of water?**
### Analysis
This thermodynamics problem can be broken down into several parts:
1. Calculate the heat required to bring the temperature of the ice from \(-15^\circ \text{C}\) to \(0^\circ \text{C}\).
2. Calculate the heat required to melt the ice at \( 0^\circ \text{C} \).
3. Calculate the heat lost by the water as it cools down to \( 0^\circ \text{C} \).
4. Determine if the heat lost by the water is enough to melt all the ice and then determine the final temperature of the system.
This problem involves the concepts of specific heat capacity and latent heat.
### Explanation
1. **Specific Heat Calculation for Ice:**
The specific heat capacity (\(c\)) of ice is \(2.1 \, \text{J/g} \cdot \text{°C}\).
Mass of ice in grams = \( 8 \times 2.5 \times 1000 = 20000 \, \text{g} \)
Heat required to bring ice from \(-15^\circ \text{C}\) to \(0^\circ \text{C}\):
\[
Q_1 = m \cdot c \cdot \Delta T = 20000 \, \text{g} \times 2.1 \, \text{J/g} \cdot \text{°C} \times (0 - (-15))\, \text{°C}
\]
2. **Latent Heat of Fusion for Ice:**
The latent heat of fusion (\(L_f\)) of ice is \(334 \, \text{J/g}\).
Heat required to melt the ice at \(0^\circ \text{C}\):
\[
Q_2 = m \cdot L_f =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9d258625-edd0-4f06-8dfd-6b1a087f7728%2F8f019668-31f7-47ed-81df-e5fbcca0b6cf%2F27jf6qd_processed.png&w=3840&q=75)
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