A
(a)
Interpretation:
The process that occurs inside the calorimeter in terms of the zeroth and first laws of thermodynamics is to be described.
Concept introduction:
The zeroth law of thermodynamics states that if system A is in thermal equilibrium with system B and system B is in thermal equilibrium with system C, then system A and system C are also in thermal equilibrium with each other. The first law of thermodynamics states that the total energy of an isolated system remains unchanged.
Answer to Problem 3.34E
In terms of the zeroth law of thermodynamics, all the systems that are in contact with each other are in equilibrium. The systems present in the calorimeter are water, copper, and walls of the calorimeter. This complete system is in thermal equilibrium.
In terms of the first of law of thermodynamics, the energy released by copper at
Explanation of Solution
The whole system of calorimeter can be divided into three systems that are water, copper metal, and the walls of the calorimeter. All these systems are in contact with each other. According to the zeroth law of thermodynamics, these systems must be in thermal equilibrium with each other.
The temperature of the water is
The temperature of copper metal is
The temperature of copper metal is higher than that of water. Therefore, to attain a thermal equilibrium, some amount of energy is lost by the copper metal and some amount of energy is gained by the water. According to the first law of thermodynamics, the energy released by copper is equal to the heat accepted by water.
In terms of the zeroth law of thermodynamics, all the systems that are in contact with each other are in equilibrium. The systems present in the calorimeter are water, copper, and the walls of the calorimeter. This complete system is in thermal equilibrium.
In terms of the first of law of thermodynamics, the energy released by copper at
(b)
Interpretation:
The final temperature inside the calorimeter system is to be calculated.
Concept introduction:
The first law of thermodynamics states that the total energy of an isolated system remains unchanged. The specific heat capacity of a substance is defined as the amount of heat required to raise the temperature of one gram of that substance by unity. The specific heat capacity of a substance is represented by the formula as shown below.
Answer to Problem 3.34E
The final temperature inside the calorimeter system is
Explanation of Solution
The initial temperature of the water is
The initial temperature of water in Kelvin is shown below.
The initial temperature of copper metal is
The initial temperature of copper metal in Kelvin is shown below.
The final temperature of both copper metal and water is the same and assumed to be
The mass of the copper metal is
The mass of water is
The specific heat capacity of water is
The specific heat capacity of copper metal is
The exchange of heat due to temperature change is represented by the expression as shown below.
Where,
•
•
•
•
In terms of the first of law of thermodynamics, the energy released by copper at
Where,
•
•
Substitute equation (1) in equation (2).
Rearrange the equation (3) for the value of
Substitute the values of initial temperature, specific heat, and masses of water and copper metal in equation (4).
Therefore, the final temperature inside the calorimeter system is
The final temperature inside the calorimeter system is
(c)
Interpretation:
The entropy change of the
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 ordered 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 3.34E
The entropy change of the
Explanation of Solution
The initial temperature of copper metal is
The initial temperature of copper metal in Kelvin is shown below.
The final temperature of copper is
The mass of the copper metal is
The specific heat capacity of copper metal is
The entropy change for the temperature change is represented by the expression as shown below.
Where,
•
•
•
•
Substitute the values of final temperature, initial temperature, specific heat, and mass of copper metal in equation (5).
Therefore, the entropy change of the
The entropy change of the
(d)
Interpretation:
The entropy change of the
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 ordered 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 3.34E
The entropy change of the
Explanation of Solution
The initial temperature of the water is
The initial temperature of water in Kelvin is shown below.
The final temperature of the water is
The mass of the water is
The specific heat capacity of water is
The entropy change for the temperature change is represented by the expression as shown below.
Where,
•
•
•
•
Substitute the values of final temperature, initial temperature, specific heat, and mass of water in equation (5).
Therefore, the entropy change of the
The entropy change of the
(e)
Interpretation:
The total entropy change in the calorimeter system 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 ordered 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 3.34E
The total entropy change in the calorimeter system is
Explanation of Solution
The entropy change of the
The entropy change of the
The total entropy change in the system is represented by the expression shown below.
Where,
•
•
Substitute the value of
Therefore, the total entropy change in the calorimeter system is
The total entropy change in the calorimeter system is
(f)
Interpretation:
The process that occurs inside the calorimeter in terms of the second law thermodynamics is to be described. Whether the corresponding process is spontaneous or not 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 ordered 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 3.34E
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 calorimeter system 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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