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A reversible thermodynamic device operates between the temperature limits of 500K, 1100K and 300K and produces 1000kJ of work. If it absorbs 500kJ of heat from Thermal reservoir of 500K, find the heat exchanged with 300K reservoir.
- a)300kJ absorbed by the device
- b)150kJ rejected by the device
- c)300kJ rejected by the device
- d)600kJ rejected by the device
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A reversible thermodynamic device operates between the temperature lim...
Let the device absorbs A amount of heat from reservoir at 1100K and B amount of heat from reservoir at 300K.
Using energy balance
A+500+B=1000
A=500-B
Using Clausius equality for a reversible device
This implies 600kJ of heat is rejected from the device.
Using energy balance
A+500+B=1000
A=500-B
Using Clausius equality for a reversible device
This implies 600kJ of heat is rejected from the device.
Most Upvoted Answer
A reversible thermodynamic device operates between the temperature lim...
Given:
- Temperature limits: 500K and 1100K
- Produced work: 1000kJ
- Heat absorbed from the 500K thermal reservoir: 500kJ
To find:
- Heat exchanged with the 300K reservoir
We can solve this problem using the concept of the Carnot cycle. The Carnot cycle is a reversible thermodynamic cycle consisting of four processes: isothermal expansion, adiabatic expansion, isothermal compression, and adiabatic compression. In a Carnot cycle, the work done is equal to the difference in heat absorbed and heat rejected.
1. Find the efficiency of the Carnot cycle:
The efficiency of a Carnot cycle is given by the formula:
Efficiency = 1 - (Tc/Th)
Where Tc is the temperature of the cold reservoir (300K) and Th is the temperature of the hot reservoir (1100K).
Efficiency = 1 - (300/1100) = 1 - 0.273 = 0.727
2. Find the heat rejected by the device:
The work done by the device is given as 1000kJ. We can calculate the heat absorbed by the device using the formula:
Work done = Heat absorbed - Heat rejected
1000kJ = 500kJ - Heat rejected
Heat rejected = 500kJ
3. Find the heat exchanged with the 300K reservoir:
Since the device operates in a Carnot cycle, the heat rejected is equal to the heat exchanged with the 300K reservoir. Therefore, the heat exchanged with the 300K reservoir is 500kJ.
Therefore, the correct answer is option 'D': 600kJ rejected by the device.
- Temperature limits: 500K and 1100K
- Produced work: 1000kJ
- Heat absorbed from the 500K thermal reservoir: 500kJ
To find:
- Heat exchanged with the 300K reservoir
We can solve this problem using the concept of the Carnot cycle. The Carnot cycle is a reversible thermodynamic cycle consisting of four processes: isothermal expansion, adiabatic expansion, isothermal compression, and adiabatic compression. In a Carnot cycle, the work done is equal to the difference in heat absorbed and heat rejected.
1. Find the efficiency of the Carnot cycle:
The efficiency of a Carnot cycle is given by the formula:
Efficiency = 1 - (Tc/Th)
Where Tc is the temperature of the cold reservoir (300K) and Th is the temperature of the hot reservoir (1100K).
Efficiency = 1 - (300/1100) = 1 - 0.273 = 0.727
2. Find the heat rejected by the device:
The work done by the device is given as 1000kJ. We can calculate the heat absorbed by the device using the formula:
Work done = Heat absorbed - Heat rejected
1000kJ = 500kJ - Heat rejected
Heat rejected = 500kJ
3. Find the heat exchanged with the 300K reservoir:
Since the device operates in a Carnot cycle, the heat rejected is equal to the heat exchanged with the 300K reservoir. Therefore, the heat exchanged with the 300K reservoir is 500kJ.
Therefore, the correct answer is option 'D': 600kJ rejected by the device.
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A reversible thermodynamic device operates between the temperature limits of 500K, 1100K and 300K and produces 1000kJ of work. If it absorbs 500kJ of heat from Thermal reservoir of 500K, find the heat exchanged with 300K reservoir.a)300kJ absorbed by the deviceb)150kJ rejected by the devicec)300kJ rejected by the deviced)600kJ rejected by the deviceCorrect answer is option 'D'. Can you explain this answer?
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