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One kg of air is subjected to the following processes:
1. Air expands isothermally from 6 bar to 3 bar.
2. Air is compressed to half the volume at constant pressure
3. Heat is supplied to air at constant volume till the pressure becomes three fold
In which of the above processes, the change in entropy will be positive?
- a)1 and 2
- b)2 and 3
- c)1 and 3
- d)1, 2 and 3
Correct answer is option 'C'. Can you explain this answer?
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Entropy is a thermodynamic property that measures the degree of disorder or randomness in a system. It is denoted by the symbol S and is related to the amount of heat transferred to or from a system and the temperature at which the transfer occurs.
In order to determine the change in entropy for each process, we need to consider the equations and principles that govern the behavior of air.
1. Isothermal Expansion (6 bar to 3 bar):
During an isothermal process, the temperature of the system remains constant. In this case, the air expands from 6 bar to 3 bar. The change in entropy for an isothermal process can be calculated using the equation:
ΔS = Q/T
Since the process is isothermal, the temperature remains constant and ΔS is directly proportional to the heat transferred, Q. As the air expands, it does work on the surroundings, so the heat transferred is negative. Thus, the change in entropy is positive.
2. Compression at Constant Pressure (Volume reduced to half):
During a constant pressure process, the pressure of the system remains constant. In this case, the air is compressed to half its volume. The change in entropy for a constant pressure process can be calculated using the equation:
ΔS = Q/T
Since the pressure remains constant, the change in entropy is directly proportional to the heat transferred, Q. As the air is compressed, work is done on the system by the surroundings, so the heat transferred is positive. Thus, the change in entropy is positive.
3. Heat Supply at Constant Volume (Pressure becomes threefold):
During a constant volume process, the volume of the system remains constant. In this case, heat is supplied to the air until the pressure becomes threefold. The change in entropy for a constant volume process can be calculated using the equation:
ΔS = Q/T
Since the volume remains constant, the change in entropy is directly proportional to the heat transferred, Q. As heat is supplied to the air, the temperature of the system increases, resulting in a positive change in entropy.
Therefore, based on the analysis of each process, it can be concluded that the change in entropy will be positive for processes 1 and 3. Thus, the correct answer is option C, "1 and 3".
In order to determine the change in entropy for each process, we need to consider the equations and principles that govern the behavior of air.
1. Isothermal Expansion (6 bar to 3 bar):
During an isothermal process, the temperature of the system remains constant. In this case, the air expands from 6 bar to 3 bar. The change in entropy for an isothermal process can be calculated using the equation:
ΔS = Q/T
Since the process is isothermal, the temperature remains constant and ΔS is directly proportional to the heat transferred, Q. As the air expands, it does work on the surroundings, so the heat transferred is negative. Thus, the change in entropy is positive.
2. Compression at Constant Pressure (Volume reduced to half):
During a constant pressure process, the pressure of the system remains constant. In this case, the air is compressed to half its volume. The change in entropy for a constant pressure process can be calculated using the equation:
ΔS = Q/T
Since the pressure remains constant, the change in entropy is directly proportional to the heat transferred, Q. As the air is compressed, work is done on the system by the surroundings, so the heat transferred is positive. Thus, the change in entropy is positive.
3. Heat Supply at Constant Volume (Pressure becomes threefold):
During a constant volume process, the volume of the system remains constant. In this case, heat is supplied to the air until the pressure becomes threefold. The change in entropy for a constant volume process can be calculated using the equation:
ΔS = Q/T
Since the volume remains constant, the change in entropy is directly proportional to the heat transferred, Q. As heat is supplied to the air, the temperature of the system increases, resulting in a positive change in entropy.
Therefore, based on the analysis of each process, it can be concluded that the change in entropy will be positive for processes 1 and 3. Thus, the correct answer is option C, "1 and 3".
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One kg of air is subjected to the following processes:1. Air expands isothermally from 6 bar to 3 bar.2. Air is compressed to half the volume at constant pressure3. Heat is supplied to air at constant volume till the pressure becomes three foldIn which of the above processes, the change in entropy will be positive?a)1 and 2b)2 and 3c)1 and 3d)1, 2 and 3Correct answer is option 'C'. Can you explain this answer?
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