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A heat transformer is device that transfers a part of the heat, supplied to it at an intermediate temperature, to a high temperature reservoir while rejecting the remaining part to a low temperature heat sink.In such a heat transformer, 100 kJ of heat is supplied at 350 K. The maximum amount of heat in kJ that can be transferred to 400 K, when the rest is rejected to a heat sink at 300 K is
[2007]
  • a)
    12.50
  • b)
    14.29
  • c)
    33.33
  • d)
    57.14
Correct answer is option 'D'. Can you explain this answer?
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A heat transformer is device that transfers a part of the heat, suppli...
Given:
- Heat supplied, Q = 100 kJ
- Temperature of heat supplied, T1 = 350 K
- Temperature of high temperature reservoir, T2 = 400 K
- Temperature of low temperature heat sink, T3 = 300 K

To find:
- Maximum amount of heat that can be transferred to T2

Concept:
- The maximum amount of heat that can be transferred from a heat source to a heat sink is given by the Carnot efficiency.
- Carnot efficiency is given by the formula: η = 1 - (T3 / T1)
- The maximum amount of heat that can be transferred to T2 is given by the formula: Q2 = η * Q

Calculation:
- Given: Q = 100 kJ, T1 = 350 K, T2 = 400 K, T3 = 300 K
- Calculate Carnot efficiency: η = 1 - (T3 / T1) = 1 - (300 / 350) = 1 - 0.857 = 0.143
- Calculate maximum heat transfer to T2: Q2 = η * Q = 0.143 * 100 = 14.29 kJ

Answer:
The maximum amount of heat that can be transferred to 400 K, when the rest is rejected to a heat sink at 300 K is 14.29 kJ. Therefore, the correct answer is option D.
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A heat transformer is device that transfers a part of the heat, supplied to it at an intermediate temperature, to a high temperature reservoir while rejecting the remaining part to a low temperature heat sink.In such a heat transformer, 100 kJ of heat is supplied at 350 K. The maximum amount of heat in kJ that can be transferred to 400 K, when the rest is rejected to a heat sink at 300 K is[2007]a)12.50b)14.29c)33.33d)57.14Correct answer is option 'D'. Can you explain this answer?
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