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A heat reservoir at 900 K is brought into contact with the ambient at 300 K for a short time. During this period 9000 kJ of heat is lost by the heat reservoir. The total loss in availability due to this process is:
- a)18000 kJ
- b)9000 kJ
- c)6000 kJ
- d)None of the above
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
A heat reservoir at 900 K is brought into contact with the ambient at ...
The availability of a thermal reservoir is equivalent to the work output of a
Carnot heat engine operating between the reservoir and the environment. Here as there is no change in the temperatures of source (reservoir) or the sink (atmosphere), the initial and final availabilities are same. Hence, there is no loss in availability.
Carnot heat engine operating between the reservoir and the environment. Here as there is no change in the temperatures of source (reservoir) or the sink (atmosphere), the initial and final availabilities are same. Hence, there is no loss in availability.
Most Upvoted Answer
A heat reservoir at 900 K is brought into contact with the ambient at ...
C)
∆Sreservoir = q/t = -9000/900 = -10kJ/K
heat lost to surrounding is 9000
∆Ssurrond. = q/t = 9000/300 = 30KJ/K
irreversibility = 300*(30-10) = 6000KJ
∆Sreservoir = q/t = -9000/900 = -10kJ/K
heat lost to surrounding is 9000
∆Ssurrond. = q/t = 9000/300 = 30KJ/K
irreversibility = 300*(30-10) = 6000KJ
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A heat reservoir at 900 K is brought into contact with the ambient at ...
Loss in availability due to the process
The availability of a system refers to the maximum useful work that can be obtained from it. When heat is transferred between two reservoirs at different temperatures, there is a loss in availability due to the irreversibility of the process.
Calculation of loss in availability
The loss in availability can be calculated using the equation:
ΔA = Q/Th - Q/Tc
Where:
ΔA = loss in availability
Q = heat transferred
Th = temperature of the hot reservoir
Tc = temperature of the cold reservoir
In this case, the heat reservoir is at 900 K and the ambient (cold reservoir) is at 300 K. The heat transfer is given as 9000 kJ.
ΔA = 9000 kJ/900 K - 9000 kJ/300 K
ΔA = 10 kJ/K - 30 kJ/K
ΔA = -20 kJ/K
Interpretation of the result
The negative sign indicates that there is a loss in availability during the heat transfer process. Since the loss in availability is -20 kJ/K, the total loss in availability due to this process can be calculated by multiplying the loss per Kelvin by the temperature difference between the hot and cold reservoirs:
Total loss in availability = ΔA * (Th - Tc)
Total loss in availability = -20 kJ/K * (900 K - 300 K)
Total loss in availability = -20 kJ/K * 600 K
Total loss in availability = -12,000 kJ
The negative sign indicates that the loss in availability is a decrease in the system's ability to do useful work. Therefore, the correct answer is option D, "None of the above."
The availability of a system refers to the maximum useful work that can be obtained from it. When heat is transferred between two reservoirs at different temperatures, there is a loss in availability due to the irreversibility of the process.
Calculation of loss in availability
The loss in availability can be calculated using the equation:
ΔA = Q/Th - Q/Tc
Where:
ΔA = loss in availability
Q = heat transferred
Th = temperature of the hot reservoir
Tc = temperature of the cold reservoir
In this case, the heat reservoir is at 900 K and the ambient (cold reservoir) is at 300 K. The heat transfer is given as 9000 kJ.
ΔA = 9000 kJ/900 K - 9000 kJ/300 K
ΔA = 10 kJ/K - 30 kJ/K
ΔA = -20 kJ/K
Interpretation of the result
The negative sign indicates that there is a loss in availability during the heat transfer process. Since the loss in availability is -20 kJ/K, the total loss in availability due to this process can be calculated by multiplying the loss per Kelvin by the temperature difference between the hot and cold reservoirs:
Total loss in availability = ΔA * (Th - Tc)
Total loss in availability = -20 kJ/K * (900 K - 300 K)
Total loss in availability = -20 kJ/K * 600 K
Total loss in availability = -12,000 kJ
The negative sign indicates that the loss in availability is a decrease in the system's ability to do useful work. Therefore, the correct answer is option D, "None of the above."
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A heat reservoir at 900 K is brought into contact with the ambient at 300 K for a short time. During this period 9000 kJ of heat is lost by the heat reservoir. The total loss in availability due to this process is:a)18000 kJb)9000 kJc)6000 kJd)None of the aboveCorrect answer is option 'D'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A heat reservoir at 900 K is brought into contact with the ambient at 300 K for a short time. During this period 9000 kJ of heat is lost by the heat reservoir. The total loss in availability due to this process is:a)18000 kJb)9000 kJc)6000 kJd)None of the aboveCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A heat reservoir at 900 K is brought into contact with the ambient at 300 K for a short time. During this period 9000 kJ of heat is lost by the heat reservoir. The total loss in availability due to this process is:a)18000 kJb)9000 kJc)6000 kJd)None of the aboveCorrect answer is option 'D'. Can you explain this answer?.
A heat reservoir at 900 K is brought into contact with the ambient at 300 K for a short time. During this period 9000 kJ of heat is lost by the heat reservoir. The total loss in availability due to this process is:a)18000 kJb)9000 kJc)6000 kJd)None of the aboveCorrect answer is option 'D'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A heat reservoir at 900 K is brought into contact with the ambient at 300 K for a short time. During this period 9000 kJ of heat is lost by the heat reservoir. The total loss in availability due to this process is:a)18000 kJb)9000 kJc)6000 kJd)None of the aboveCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A heat reservoir at 900 K is brought into contact with the ambient at 300 K for a short time. During this period 9000 kJ of heat is lost by the heat reservoir. The total loss in availability due to this process is:a)18000 kJb)9000 kJc)6000 kJd)None of the aboveCorrect answer is option 'D'. Can you explain this answer?.
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