A sample of
(a)
Interpretation:
The final temperature of the hot and cold silver is to be calculated.
Concept introduction:
The first law of thermodynamics states that the total energy of an isolated system remains unchanged. The molar heat capacity of a substance is defined as the amount of heat required to raise the temperature of one mole of that substance by unity. The molar heat capacity of a substance is shown below.
Answer to Problem 3.35E
The final temperature of the hot and cold silver is
Explanation of Solution
The initial temperature of the hot silver is
The initial temperature of hot silver in Kelvin is shown below.
The initial temperature of cold silver is
The initial temperature of cold silver in Kelvin is shown below as,
The final temperature of both cold silver and hot silver is the same and assumed to be
The number of moles of both cold and hot silver is
The molar heat capacity of silver is
The exchange of heat due to temperature change is shown below.
Where,
•
•
•
•
In terms of the first of law of thermodynamics, the energy released by hot silver is equal to the heat accepted by cold silver. The relationship between heat exchanges is shown below.
Where,
•
•
Substitute equation (1) in equation (2).
Rearrange the equation (3) for the value of
Substitute the values of initial temperature, molar heat capacity and number of moles of hot silver and cold silver in equation (4).
The final temperature of the hot and cold silver is
The final temperature of the hot and cold silver in degree Celsius is represented as,
Therefore, the final temperature of the hot and cold silver is
The final temperature of the hot and cold silver is
(b)
Interpretation:
The entropy change of the hot
Concept introduction:
The term entropy is used to represent the randomness in a system. When a system moves from an ordered arrangement to a less order arrangement, then the entropy of the system increases. The second law of thermodynamics states that the entropy of the system either increases or remains the same.
Answer to Problem 3.35E
The entropy change of hot
Explanation of Solution
The initial temperature of the hot silver is
The initial temperature of hot silver in Kelvin is shown below.
The final temperature of the hot silver is
The number of moles of hot silver is
The molar heat capacity of silver is
The entropy change for the temperature change is shown below.
Where,
•
•
•
•
Substitute the values of final temperature, initial temperature, molar heat capacity and mass of hot silver in equation (5).
Therefore, the entropy change of the hot
The entropy change of hot
(c)
Interpretation:
The entropy change of the cold silver sample is to be calculated.
Concept introduction:
The term entropy is used to represent the randomness in a system. When a system moves from an ordered arrangement to a less order arrangement, then the entropy of the system increases. The second law of thermodynamics states that the entropy of the system either increases or remains the same.
Answer to Problem 3.35E
The entropy change of the cold
Explanation of Solution
The initial temperature of cold silver is
The initial temperature of cold silver in Kelvin is shown below.
The final temperature of the cold silver is
The number of moles of cold silver is
The molar heat capacity of silver is
The entropy change for the temperature change is shown below.
Where,
•
•
•
•
Substitute the values of final temperature, initial temperature, molar heat capacity and mass of cold silver in equation (5).
Therefore, the entropy change of the cold
The entropy change of the cold
(d)
Interpretation:
The total entropy change in the system of silver is to be calculated.
Concept introduction:
The term entropy is used to represent the randomness in a system. When a system moves from an ordered arrangement to a less order arrangement, then the entropy of the system increases. The second law of thermodynamics states that the entropy of the system either increases or remains the same.
Answer to Problem 3.35E
The total entropy change in the system of silver is
Explanation of Solution
The entropy change of hot
The entropy change of the cold
The total entropy change of the given mixture is shown below.
Where,
•
•
Substitute the values of
Therefore, the total entropy change in the system of silver is
The total entropy change in the system of silver is
(e)
Interpretation:
Whether the process of heat exchange is spontaneous or not is to be stated. The reason for the corresponding answer is to be stated.
Concept introduction:
The term entropy is used to represent the randomness in a system. When a system moves from an ordered arrangement to a less order arrangement, then the entropy of the system increases. The second law of thermodynamics state that the entropy of the system either increases or remain the same.
Answer to Problem 3.35E
The process is spontaneous because the entropy change of the system is positive. According to the second law of thermodynamics, the entropy change of system must be positive for a spontaneous process.
Explanation of Solution
The total entropy change in the system of silver is
This value implies that the randomness in the system is increasing with time. The second law of thermodynamics states that the entropy of the system either increases or remains the same. The entropy change is positive that means the entropy of the system is increasing. Therefore, the process is spontaneous.
The process is spontaneous because the entropy change of the system is positive. According to the second law of thermodynamics, the entropy change of system must be positive for a spontaneous process.
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Chapter 3 Solutions
Physical Chemistry
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