Wärmepumpe im Winter
About points...
We associate a certain number of points with each exercise.
When you click an exercise into a collection, this number will be taken as points for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit the number of points for the exercise in the collection independently, without any effect on "points by default" as represented by the number here.
That being said... How many "default points" should you associate with an exercise upon creation?
As with difficulty, there is no straight forward and generally accepted way.
But as a guideline, we tend to give as many points by default as there are mathematical steps to do in the exercise.
Again, very vague... But the number should kind of represent the "work" required.
When you click an exercise into a collection, this number will be taken as points for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit the number of points for the exercise in the collection independently, without any effect on "points by default" as represented by the number here.
That being said... How many "default points" should you associate with an exercise upon creation?
As with difficulty, there is no straight forward and generally accepted way.
But as a guideline, we tend to give as many points by default as there are mathematical steps to do in the exercise.
Again, very vague... But the number should kind of represent the "work" required.
About difficulty...
We associate a certain difficulty with each exercise.
When you click an exercise into a collection, this number will be taken as difficulty for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit its difficulty in the collection independently, without any effect on the "difficulty by default" here.
Why we use chess pieces? Well... we like chess, we like playing around with \(\LaTeX\)-fonts, we wanted symbols that need less space than six stars in a table-column... But in your layouts, you are of course free to indicate the difficulty of the exercise the way you want.
That being said... How "difficult" is an exercise? It depends on many factors, like what was being taught etc.
In physics exercises, we try to follow this pattern:
Level 1 - One formula (one you would find in a reference book) is enough to solve the exercise. Example exercise
Level 2 - Two formulas are needed, it's possible to compute an "in-between" solution, i.e. no algebraic equation needed. Example exercise
Level 3 - "Chain-computations" like on level 2, but 3+ calculations. Still, no equations, i.e. you are not forced to solve it in an algebraic manner. Example exercise
Level 4 - Exercise needs to be solved by algebraic equations, not possible to calculate numerical "in-between" results. Example exercise
Level 5 -
Level 6 -
When you click an exercise into a collection, this number will be taken as difficulty for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit its difficulty in the collection independently, without any effect on the "difficulty by default" here.
Why we use chess pieces? Well... we like chess, we like playing around with \(\LaTeX\)-fonts, we wanted symbols that need less space than six stars in a table-column... But in your layouts, you are of course free to indicate the difficulty of the exercise the way you want.
That being said... How "difficult" is an exercise? It depends on many factors, like what was being taught etc.
In physics exercises, we try to follow this pattern:
Level 1 - One formula (one you would find in a reference book) is enough to solve the exercise. Example exercise
Level 2 - Two formulas are needed, it's possible to compute an "in-between" solution, i.e. no algebraic equation needed. Example exercise
Level 3 - "Chain-computations" like on level 2, but 3+ calculations. Still, no equations, i.e. you are not forced to solve it in an algebraic manner. Example exercise
Level 4 - Exercise needs to be solved by algebraic equations, not possible to calculate numerical "in-between" results. Example exercise
Level 5 -
Level 6 -
Question
Solution
Short
Video
\(\LaTeX\)
Need help? Yes, please!
The following quantities appear in the problem:
Zeit \(t\) / Temperatur \(T\) / Arbeit \(W\) / Energie \(E\) / Leistung \(P, \Phi\) / Wärme \(Q\) / Verhältnis / Anteil \(\eta\) / Leistungszahl \(\epsilon\) /
The following formulas must be used to solve the exercise:
\(\eta = \dfrac{a}{A} \quad \) \(\varepsilon = \dfrac{T_H}{T_H-T_L} \quad \) \(P = \dfrac{E}{t} = \dfrac{W}{t} = \dfrac{Q}{t} \quad \) \(\epsilon = \frac{Q_H}{W} \quad \) \(\epsilon = \frac{Q_H}{Q_H-Q_L} \quad \)
No explanation / solution video to this exercise has yet been created.
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Visit our YouTube-Channel to see solutions to other exercises.
Don't forget to subscribe to our channel, like the videos and leave comments!
Exercise:
Eine Wärmepumpe führe der Heizung eines Hauses eine Leistung von PO zu. Die Aussentemperatur betrage TkO und die Temperatur des Heizkessels liege bei TwO. abcliste abc Wie hoch ist die Leistungszahl wenn die Maschine vollkommen reversibel arbeitet? abc Mit welcher Leistung muss sie mindestens betrieben werden? abcliste
Solution:
Geg P PO P T_k Tk T_w Tw GesLeistungszahlepsilon_WP Gesminimale LeistungP_minsiwatt abcliste abc Die Leistungszahl einer Wärmepumpe ist T_w TwKF Tw + . TwK T_k TkKF Tk + . TkK epsilon_WP fracT_wT_w - T_k fracTwKFTwKF - TkKF epwF fracTw - -fracTw - Tk epw approx epwP epsilon_WP epwF epwP abc Um eine bestimmte Wärme Q_w an das wärmere Reservoir abzugeben ist die Arbeit W fracQ_wepsilon_WP erforderlich. Dem entspricht eine Leistung von P_min fracPepsilon_WP fracPepwF PminF fracP leftTw + . - Tk + .rightTw + . Pmin approx PminP P_min PminF PminP abcliste
Eine Wärmepumpe führe der Heizung eines Hauses eine Leistung von PO zu. Die Aussentemperatur betrage TkO und die Temperatur des Heizkessels liege bei TwO. abcliste abc Wie hoch ist die Leistungszahl wenn die Maschine vollkommen reversibel arbeitet? abc Mit welcher Leistung muss sie mindestens betrieben werden? abcliste
Solution:
Geg P PO P T_k Tk T_w Tw GesLeistungszahlepsilon_WP Gesminimale LeistungP_minsiwatt abcliste abc Die Leistungszahl einer Wärmepumpe ist T_w TwKF Tw + . TwK T_k TkKF Tk + . TkK epsilon_WP fracT_wT_w - T_k fracTwKFTwKF - TkKF epwF fracTw - -fracTw - Tk epw approx epwP epsilon_WP epwF epwP abc Um eine bestimmte Wärme Q_w an das wärmere Reservoir abzugeben ist die Arbeit W fracQ_wepsilon_WP erforderlich. Dem entspricht eine Leistung von P_min fracPepsilon_WP fracPepwF PminF fracP leftTw + . - Tk + .rightTw + . Pmin approx PminP P_min PminF PminP abcliste
Meta Information
Exercise:
Eine Wärmepumpe führe der Heizung eines Hauses eine Leistung von PO zu. Die Aussentemperatur betrage TkO und die Temperatur des Heizkessels liege bei TwO. abcliste abc Wie hoch ist die Leistungszahl wenn die Maschine vollkommen reversibel arbeitet? abc Mit welcher Leistung muss sie mindestens betrieben werden? abcliste
Solution:
Geg P PO P T_k Tk T_w Tw GesLeistungszahlepsilon_WP Gesminimale LeistungP_minsiwatt abcliste abc Die Leistungszahl einer Wärmepumpe ist T_w TwKF Tw + . TwK T_k TkKF Tk + . TkK epsilon_WP fracT_wT_w - T_k fracTwKFTwKF - TkKF epwF fracTw - -fracTw - Tk epw approx epwP epsilon_WP epwF epwP abc Um eine bestimmte Wärme Q_w an das wärmere Reservoir abzugeben ist die Arbeit W fracQ_wepsilon_WP erforderlich. Dem entspricht eine Leistung von P_min fracPepsilon_WP fracPepwF PminF fracP leftTw + . - Tk + .rightTw + . Pmin approx PminP P_min PminF PminP abcliste
Eine Wärmepumpe führe der Heizung eines Hauses eine Leistung von PO zu. Die Aussentemperatur betrage TkO und die Temperatur des Heizkessels liege bei TwO. abcliste abc Wie hoch ist die Leistungszahl wenn die Maschine vollkommen reversibel arbeitet? abc Mit welcher Leistung muss sie mindestens betrieben werden? abcliste
Solution:
Geg P PO P T_k Tk T_w Tw GesLeistungszahlepsilon_WP Gesminimale LeistungP_minsiwatt abcliste abc Die Leistungszahl einer Wärmepumpe ist T_w TwKF Tw + . TwK T_k TkKF Tk + . TkK epsilon_WP fracT_wT_w - T_k fracTwKFTwKF - TkKF epwF fracTw - -fracTw - Tk epw approx epwP epsilon_WP epwF epwP abc Um eine bestimmte Wärme Q_w an das wärmere Reservoir abzugeben ist die Arbeit W fracQ_wepsilon_WP erforderlich. Dem entspricht eine Leistung von P_min fracPepsilon_WP fracPepwF PminF fracP leftTw + . - Tk + .rightTw + . Pmin approx PminP P_min PminF PminP abcliste
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Reale vs. ideale Leistungszahl bei Wärmepumpe by TeXercises
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