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https://texercises.com/exercise/compressor-of-a-heat-pump/
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The following quantities appear in the problem: Temperatur \(T\) / Wärme \(Q\) / Leistungszahl \(\epsilon\) /
The following formulas must be used to solve the exercise: \(\varepsilon = \dfrac{T_H}{T_H-T_L} \quad \) \(\epsilon = \frac{Q_H}{Q_H-Q_L} \quad \)
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Exercise:
A heat pump provides PwO heating output at twO target temperature and tkO ambient temperature. What is the minimum electrical power that must be supplied to the compressor?

Solution:
Geg sscPH PwO Pw theta_H taO to sscTH Tw theta_L taO to sscTL Tk GesElectric PowerPsiW SolQtyeTwX/TwX-TkX At best the heat pump has epsilon fracsscTHsscTH-sscTL fracTwTw-Tk e efficiency which means that at least SolQtyPPwX/eXW P fracsscPHepsilon fracsscTH-sscTLepsilonsscTH fracPwe P approx PS PP of electrical power must be provided. P fracsscTH-sscTLepsilonsscTH PS PP
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Exercise:
A heat pump provides PwO heating output at twO target temperature and tkO ambient temperature. What is the minimum electrical power that must be supplied to the compressor?

Solution:
Geg sscPH PwO Pw theta_H taO to sscTH Tw theta_L taO to sscTL Tk GesElectric PowerPsiW SolQtyeTwX/TwX-TkX At best the heat pump has epsilon fracsscTHsscTH-sscTL fracTwTw-Tk e efficiency which means that at least SolQtyPPwX/eXW P fracsscPHepsilon fracsscTH-sscTLepsilonsscTH fracPwe P approx PS PP of electrical power must be provided. P fracsscTH-sscTLepsilonsscTH PS PP
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Attributes & Decorations
Asked Quantity
Branches
Work, Energy, Power
Tags
kreisprozess, leistung, leistungszahl, physik, temperatur, thermodynamik, wärmepumpe
Difficulty
(2, default)
Points
2 (default)
Language
ENG (English)
Type
Calculative / Quantity
Decoration
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