Geschwindigkeit, Energie und Impuls eines Gasteilchens
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 Wasserstoffgas hat die Temperatur Ta bzw. Tb. Verwen Sie folge Näherung: al Aboxedoverlinev^ overlinev^ abcliste abc Wie gross ist die mittlere kinetische Energie und der mittlere Impuls eines ceH-Moleküls? abc Welcher Impuls wird von einem ceH-Teilchen beim senkrechten elastischen Stoss auf die Wand übertragen? abc Welche Energie steckt in einem Mol ceH-Gas? abcliste
Solution:
abcliste abc overlinesscEKin frac k T frac sscmT overlinev^ overlinev vaF overlinev sqrt kB fracTaKmT U overlinev va approx vaS overlinev vbF overlinev sqrt kB fracTbKmT U overlinev vb approx vbS abc overlinesscEKin EkinaF overlinesscEKin frac kB TaK overlinesscEKin Ekina approx EkinaS overlinesscEKin EkinbF overlinesscEKin frac kB TbK overlinesscEKin Ekina approx EkinbS overlinep sscmT overlinev paF overlinep sqrt kB TaK mT U overlinep pa approx paS overlinep sscmT overlinev pbF overlinep sqrt kB TbK mT U overlinep pb approx pbS abc Beim elastischen Stoss wird das Teilchen durch die Wand zuerst abgebremst und dann wieder in die Gegenrichtung beschleunigt. Damit ändert der Impuls um den doppelten Betrag des anfänglichen Impulses. Delta p DpaF Delta p pa Delta p Dpa approx DpaS Delta p DpbF Delta p pb Delta p Dpb approx DpbS abc E EtotaF E NA MZ Ekina E Etota approx EtotaS E EtotbF E NA MZ Ekinb E Etotb approx EtotbS abcliste
Ein Wasserstoffgas hat die Temperatur Ta bzw. Tb. Verwen Sie folge Näherung: al Aboxedoverlinev^ overlinev^ abcliste abc Wie gross ist die mittlere kinetische Energie und der mittlere Impuls eines ceH-Moleküls? abc Welcher Impuls wird von einem ceH-Teilchen beim senkrechten elastischen Stoss auf die Wand übertragen? abc Welche Energie steckt in einem Mol ceH-Gas? abcliste
Solution:
abcliste abc overlinesscEKin frac k T frac sscmT overlinev^ overlinev vaF overlinev sqrt kB fracTaKmT U overlinev va approx vaS overlinev vbF overlinev sqrt kB fracTbKmT U overlinev vb approx vbS abc overlinesscEKin EkinaF overlinesscEKin frac kB TaK overlinesscEKin Ekina approx EkinaS overlinesscEKin EkinbF overlinesscEKin frac kB TbK overlinesscEKin Ekina approx EkinbS overlinep sscmT overlinev paF overlinep sqrt kB TaK mT U overlinep pa approx paS overlinep sscmT overlinev pbF overlinep sqrt kB TbK mT U overlinep pb approx pbS abc Beim elastischen Stoss wird das Teilchen durch die Wand zuerst abgebremst und dann wieder in die Gegenrichtung beschleunigt. Damit ändert der Impuls um den doppelten Betrag des anfänglichen Impulses. Delta p DpaF Delta p pa Delta p Dpa approx DpaS Delta p DpbF Delta p pb Delta p Dpb approx DpbS abc E EtotaF E NA MZ Ekina E Etota approx EtotaS E EtotbF E NA MZ Ekinb E Etotb approx EtotbS abcliste
Meta Information
Exercise:
Ein Wasserstoffgas hat die Temperatur Ta bzw. Tb. Verwen Sie folge Näherung: al Aboxedoverlinev^ overlinev^ abcliste abc Wie gross ist die mittlere kinetische Energie und der mittlere Impuls eines ceH-Moleküls? abc Welcher Impuls wird von einem ceH-Teilchen beim senkrechten elastischen Stoss auf die Wand übertragen? abc Welche Energie steckt in einem Mol ceH-Gas? abcliste
Solution:
abcliste abc overlinesscEKin frac k T frac sscmT overlinev^ overlinev vaF overlinev sqrt kB fracTaKmT U overlinev va approx vaS overlinev vbF overlinev sqrt kB fracTbKmT U overlinev vb approx vbS abc overlinesscEKin EkinaF overlinesscEKin frac kB TaK overlinesscEKin Ekina approx EkinaS overlinesscEKin EkinbF overlinesscEKin frac kB TbK overlinesscEKin Ekina approx EkinbS overlinep sscmT overlinev paF overlinep sqrt kB TaK mT U overlinep pa approx paS overlinep sscmT overlinev pbF overlinep sqrt kB TbK mT U overlinep pb approx pbS abc Beim elastischen Stoss wird das Teilchen durch die Wand zuerst abgebremst und dann wieder in die Gegenrichtung beschleunigt. Damit ändert der Impuls um den doppelten Betrag des anfänglichen Impulses. Delta p DpaF Delta p pa Delta p Dpa approx DpaS Delta p DpbF Delta p pb Delta p Dpb approx DpbS abc E EtotaF E NA MZ Ekina E Etota approx EtotaS E EtotbF E NA MZ Ekinb E Etotb approx EtotbS abcliste
Ein Wasserstoffgas hat die Temperatur Ta bzw. Tb. Verwen Sie folge Näherung: al Aboxedoverlinev^ overlinev^ abcliste abc Wie gross ist die mittlere kinetische Energie und der mittlere Impuls eines ceH-Moleküls? abc Welcher Impuls wird von einem ceH-Teilchen beim senkrechten elastischen Stoss auf die Wand übertragen? abc Welche Energie steckt in einem Mol ceH-Gas? abcliste
Solution:
abcliste abc overlinesscEKin frac k T frac sscmT overlinev^ overlinev vaF overlinev sqrt kB fracTaKmT U overlinev va approx vaS overlinev vbF overlinev sqrt kB fracTbKmT U overlinev vb approx vbS abc overlinesscEKin EkinaF overlinesscEKin frac kB TaK overlinesscEKin Ekina approx EkinaS overlinesscEKin EkinbF overlinesscEKin frac kB TbK overlinesscEKin Ekina approx EkinbS overlinep sscmT overlinev paF overlinep sqrt kB TaK mT U overlinep pa approx paS overlinep sscmT overlinev pbF overlinep sqrt kB TbK mT U overlinep pb approx pbS abc Beim elastischen Stoss wird das Teilchen durch die Wand zuerst abgebremst und dann wieder in die Gegenrichtung beschleunigt. Damit ändert der Impuls um den doppelten Betrag des anfänglichen Impulses. Delta p DpaF Delta p pa Delta p Dpa approx DpaS Delta p DpbF Delta p pb Delta p Dpb approx DpbS abc E EtotaF E NA MZ Ekina E Etota approx EtotaS E EtotbF E NA MZ Ekinb E Etotb approx EtotbS abcliste
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Kinetische Gastheorie by dk