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A house that is losing heat at a rate of 60,000 kJ/hr when the outside temperature drops to 4 °C, is to be heated by electric resistance heaters. If the house is to be maintained at 24 °C at all times, then the irreversibility (in kW) of this process is
- a)5.86
- b)12.56
- c)25.56
- d)15.55
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A house that is losing heat at a rate of 60,000 kJ/hr when the outsid...
The reversible work is the minimum work required to accomplish this process, and the irreversibility is the difference between the reversible work and the actual electrical work consumed.
Actual power input
Woct'in = Qout = QH=60000 kj/h
=16.67 kW
COP of a reversible heat pump
=1.1225 kW
I=Woct.in - Wrev.in
=16.67-1.1225
=15.55 kW
Most Upvoted Answer
A house that is losing heat at a rate of 60,000 kJ/hr when the outsid...
To calculate the irreversibility of the process, we need to determine the heat transfer and the temperature difference between the house and the surroundings.
Given:
Heat loss rate = 60,000 kJ/hr
Outside temperature (T_out) = 4 °C
Inside temperature (T_in) = 24 °C
Step 1: Calculate the heat transfer rate
The heat transfer rate can be calculated using the formula:
Q = U * A * ΔT
Where:
Q is the heat transfer rate
U is the overall heat transfer coefficient
A is the surface area of the house
ΔT is the temperature difference between the house and the surroundings
Since we are given the heat loss rate, we can rearrange the formula to solve for U * A:
U * A = Q / ΔT
Step 2: Calculate the temperature difference
The temperature difference can be calculated as:
ΔT = T_in - T_out
Step 3: Calculate the irreversibility
The irreversibility can be calculated using the formula:
Irreversibility = Q * (1 - T_out / T_in)
Substituting the values:
ΔT = 24 °C - 4 °C = 20 °C
U * A = (60,000 kJ/hr) / (20 °C)
= 3,000 kJ/hr°C
Irreversibility = (60,000 kJ/hr) * (1 - 4 °C / 24 °C)
= (60,000 kJ/hr) * (1 - 1/6)
= (60,000 kJ/hr) * (5/6)
= 50,000 kJ/hr
Converting the irreversibility to kW:
Irreversibility = 50,000 kJ/hr * (1 kW / 3.6 kJ/s)
= 13,888.8 W
≈ 13.89 kW
Therefore, the correct answer is option D) 15.55 kW.
Given:
Heat loss rate = 60,000 kJ/hr
Outside temperature (T_out) = 4 °C
Inside temperature (T_in) = 24 °C
Step 1: Calculate the heat transfer rate
The heat transfer rate can be calculated using the formula:
Q = U * A * ΔT
Where:
Q is the heat transfer rate
U is the overall heat transfer coefficient
A is the surface area of the house
ΔT is the temperature difference between the house and the surroundings
Since we are given the heat loss rate, we can rearrange the formula to solve for U * A:
U * A = Q / ΔT
Step 2: Calculate the temperature difference
The temperature difference can be calculated as:
ΔT = T_in - T_out
Step 3: Calculate the irreversibility
The irreversibility can be calculated using the formula:
Irreversibility = Q * (1 - T_out / T_in)
Substituting the values:
ΔT = 24 °C - 4 °C = 20 °C
U * A = (60,000 kJ/hr) / (20 °C)
= 3,000 kJ/hr°C
Irreversibility = (60,000 kJ/hr) * (1 - 4 °C / 24 °C)
= (60,000 kJ/hr) * (1 - 1/6)
= (60,000 kJ/hr) * (5/6)
= 50,000 kJ/hr
Converting the irreversibility to kW:
Irreversibility = 50,000 kJ/hr * (1 kW / 3.6 kJ/s)
= 13,888.8 W
≈ 13.89 kW
Therefore, the correct answer is option D) 15.55 kW.
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A house that is losing heat at a rate of 60,000 kJ/hr when the outside temperature drops to 4 °C, is to be heated by electric resistance heaters. If the house is to be maintained at 24 °C at all times, then the irreversibility (in kW) of this process isa)5.86b)12.56c)25.56d)15.55Correct answer is option 'D'. Can you explain this answer?
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A house that is losing heat at a rate of 60,000 kJ/hr when the outside temperature drops to 4 °C, is to be heated by electric resistance heaters. If the house is to be maintained at 24 °C at all times, then the irreversibility (in kW) of this process isa)5.86b)12.56c)25.56d)15.55Correct answer is option 'D'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A house that is losing heat at a rate of 60,000 kJ/hr when the outside temperature drops to 4 °C, is to be heated by electric resistance heaters. If the house is to be maintained at 24 °C at all times, then the irreversibility (in kW) of this process isa)5.86b)12.56c)25.56d)15.55Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A house that is losing heat at a rate of 60,000 kJ/hr when the outside temperature drops to 4 °C, is to be heated by electric resistance heaters. If the house is to be maintained at 24 °C at all times, then the irreversibility (in kW) of this process isa)5.86b)12.56c)25.56d)15.55Correct answer is option 'D'. Can you explain this answer?.
A house that is losing heat at a rate of 60,000 kJ/hr when the outside temperature drops to 4 °C, is to be heated by electric resistance heaters. If the house is to be maintained at 24 °C at all times, then the irreversibility (in kW) of this process isa)5.86b)12.56c)25.56d)15.55Correct answer is option 'D'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A house that is losing heat at a rate of 60,000 kJ/hr when the outside temperature drops to 4 °C, is to be heated by electric resistance heaters. If the house is to be maintained at 24 °C at all times, then the irreversibility (in kW) of this process isa)5.86b)12.56c)25.56d)15.55Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A house that is losing heat at a rate of 60,000 kJ/hr when the outside temperature drops to 4 °C, is to be heated by electric resistance heaters. If the house is to be maintained at 24 °C at all times, then the irreversibility (in kW) of this process isa)5.86b)12.56c)25.56d)15.55Correct answer is option 'D'. Can you explain this answer?.
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