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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 these
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
A heat reservoir at 900 K is brought into contact with the ambient at ...
Entropy change for hot reservoir
Energy gain in cold reservoir
Loss in availability = T0 [ ΔSc + ΔSh ]
⇒ 300(30 – 10)
= 300(20)
= 6000 kJ
Energy gain in cold reservoir
Loss in availability = T0 [ ΔSc + ΔSh ]
⇒ 300(30 – 10)
= 300(20)
= 6000 kJ
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A heat reservoir at 900 K is brought into contact with the ambient at ...
Loss in Availability Due to Heat Transfer
When a heat reservoir at a high temperature T1 is brought into contact with a heat sink at a lower temperature T2, heat will flow from the reservoir to the sink. The amount of heat transferred is given by:
Q = mC(T1 - T2)
where Q is the heat transferred, m is the mass of the substance, C is the specific heat capacity, and T1 and T2 are the temperatures of the reservoir and sink, respectively.
However, not all of the heat transferred is useful. Some of it is lost in the form of entropy. The amount of heat that can be converted to work is given by the change in availability:
A = Q - TS
where S is the entropy change and T is the temperature at which the transfer occurs. The change in availability is a measure of the useful work that can be obtained from the heat transfer.
Calculation of Loss in Availability
Given:
T1 = 900 K
T2 = 300 K
Q = 9000 kJ
We can calculate the change in entropy using the formula:
ΔS = Q/T
where Q is the heat transferred and T is the temperature at which the transfer occurs. Substituting the values, we get:
ΔS = 9000 kJ / 900 K = 10 kJ/K
The loss in availability is then given by:
A = Q - TS
A = 9000 kJ - 300 K * 10 kJ/K
A = 6000 kJ
Therefore, the total loss in availability due to the heat transfer is 6000 kJ.
When a heat reservoir at a high temperature T1 is brought into contact with a heat sink at a lower temperature T2, heat will flow from the reservoir to the sink. The amount of heat transferred is given by:
Q = mC(T1 - T2)
where Q is the heat transferred, m is the mass of the substance, C is the specific heat capacity, and T1 and T2 are the temperatures of the reservoir and sink, respectively.
However, not all of the heat transferred is useful. Some of it is lost in the form of entropy. The amount of heat that can be converted to work is given by the change in availability:
A = Q - TS
where S is the entropy change and T is the temperature at which the transfer occurs. The change in availability is a measure of the useful work that can be obtained from the heat transfer.
Calculation of Loss in Availability
Given:
T1 = 900 K
T2 = 300 K
Q = 9000 kJ
We can calculate the change in entropy using the formula:
ΔS = Q/T
where Q is the heat transferred and T is the temperature at which the transfer occurs. Substituting the values, we get:
ΔS = 9000 kJ / 900 K = 10 kJ/K
The loss in availability is then given by:
A = Q - TS
A = 9000 kJ - 300 K * 10 kJ/K
A = 6000 kJ
Therefore, the total loss in availability due to the heat transfer is 6000 kJ.
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Question Description
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 isa)18000 kJb)9000 kJc)6000 kJd)None of theseCorrect answer is option 'C'. 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 isa)18000 kJb)9000 kJc)6000 kJd)None of theseCorrect answer is option 'C'. 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 isa)18000 kJb)9000 kJc)6000 kJd)None of theseCorrect answer is option 'C'. 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 isa)18000 kJb)9000 kJc)6000 kJd)None of theseCorrect answer is option 'C'. 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 isa)18000 kJb)9000 kJc)6000 kJd)None of theseCorrect answer is option 'C'. 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 isa)18000 kJb)9000 kJc)6000 kJd)None of theseCorrect answer is option 'C'. Can you explain this answer?.
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