Adiabatischer Prozess
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
\(\LaTeX\)
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Exercise:
Ein Velopneu enthalte Luft unter einem absoluten Druck von .sibar bei sicelsius. Als der Schlauch platzt wird der Pneudruck schlagartig zehnmal kleiner. Auf welchen Wert sinkt die Temperatur?
Solution:
Das Verb ``platzen'' deutet auf einen schnellen Vorgang hin währ dem kein Temperaturausgleich mit der Umgebung stattfindet. Es gelten also die Gesetze der adiabatischen Expansion. Da wir nur Adiabatengleichungen mit dem Volumen hergeleitet haben müssen wir das Volumen ersetzen. Dies tun wir mit der Zustandsgleichung des idealen Gases. Es gilt: pV^kappa pleftfracnRTpright^kappa myRarrow fracpp^kappaT^kappa konst wobei wir aus pVnRT V fracnRTp eingesetzt haben. * &p^-varkappaT^varkappa textconst Rightarrow fracT_^varkappap_^varkappa- fracT_^varkappap_^varkappa- Rightarrow left fracT_T_ right^varkappa left fracp_p_ right^varkappa - Rightarrow &T_ T_ left fracp_p_ right^fracvarkappa -varkappa .+siK left frac right^frac. -. .siK hat uuline -sicelsius * Die Temperatur ist eher als untere Grenze zu verstehen.
Ein Velopneu enthalte Luft unter einem absoluten Druck von .sibar bei sicelsius. Als der Schlauch platzt wird der Pneudruck schlagartig zehnmal kleiner. Auf welchen Wert sinkt die Temperatur?
Solution:
Das Verb ``platzen'' deutet auf einen schnellen Vorgang hin währ dem kein Temperaturausgleich mit der Umgebung stattfindet. Es gelten also die Gesetze der adiabatischen Expansion. Da wir nur Adiabatengleichungen mit dem Volumen hergeleitet haben müssen wir das Volumen ersetzen. Dies tun wir mit der Zustandsgleichung des idealen Gases. Es gilt: pV^kappa pleftfracnRTpright^kappa myRarrow fracpp^kappaT^kappa konst wobei wir aus pVnRT V fracnRTp eingesetzt haben. * &p^-varkappaT^varkappa textconst Rightarrow fracT_^varkappap_^varkappa- fracT_^varkappap_^varkappa- Rightarrow left fracT_T_ right^varkappa left fracp_p_ right^varkappa - Rightarrow &T_ T_ left fracp_p_ right^fracvarkappa -varkappa .+siK left frac right^frac. -. .siK hat uuline -sicelsius * Die Temperatur ist eher als untere Grenze zu verstehen.
Meta Information
Exercise:
Ein Velopneu enthalte Luft unter einem absoluten Druck von .sibar bei sicelsius. Als der Schlauch platzt wird der Pneudruck schlagartig zehnmal kleiner. Auf welchen Wert sinkt die Temperatur?
Solution:
Das Verb ``platzen'' deutet auf einen schnellen Vorgang hin währ dem kein Temperaturausgleich mit der Umgebung stattfindet. Es gelten also die Gesetze der adiabatischen Expansion. Da wir nur Adiabatengleichungen mit dem Volumen hergeleitet haben müssen wir das Volumen ersetzen. Dies tun wir mit der Zustandsgleichung des idealen Gases. Es gilt: pV^kappa pleftfracnRTpright^kappa myRarrow fracpp^kappaT^kappa konst wobei wir aus pVnRT V fracnRTp eingesetzt haben. * &p^-varkappaT^varkappa textconst Rightarrow fracT_^varkappap_^varkappa- fracT_^varkappap_^varkappa- Rightarrow left fracT_T_ right^varkappa left fracp_p_ right^varkappa - Rightarrow &T_ T_ left fracp_p_ right^fracvarkappa -varkappa .+siK left frac right^frac. -. .siK hat uuline -sicelsius * Die Temperatur ist eher als untere Grenze zu verstehen.
Ein Velopneu enthalte Luft unter einem absoluten Druck von .sibar bei sicelsius. Als der Schlauch platzt wird der Pneudruck schlagartig zehnmal kleiner. Auf welchen Wert sinkt die Temperatur?
Solution:
Das Verb ``platzen'' deutet auf einen schnellen Vorgang hin währ dem kein Temperaturausgleich mit der Umgebung stattfindet. Es gelten also die Gesetze der adiabatischen Expansion. Da wir nur Adiabatengleichungen mit dem Volumen hergeleitet haben müssen wir das Volumen ersetzen. Dies tun wir mit der Zustandsgleichung des idealen Gases. Es gilt: pV^kappa pleftfracnRTpright^kappa myRarrow fracpp^kappaT^kappa konst wobei wir aus pVnRT V fracnRTp eingesetzt haben. * &p^-varkappaT^varkappa textconst Rightarrow fracT_^varkappap_^varkappa- fracT_^varkappap_^varkappa- Rightarrow left fracT_T_ right^varkappa left fracp_p_ right^varkappa - Rightarrow &T_ T_ left fracp_p_ right^fracvarkappa -varkappa .+siK left frac right^frac. -. .siK hat uuline -sicelsius * Die Temperatur ist eher als untere Grenze zu verstehen.
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