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Gas tank in the sun

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".
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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 -

Exercise

https://texercises.com/exercise/gas-tank-in-the-sun/

Question

Solution

Short

Video

\(\LaTeX\)

Need help? Yes, please!

The following quantities appear in the problem: Temperatur \(T\) / Volumen \(V\) / Längenausdehnungskoeffizient \(\alpha\) / Volumenausdehnungskoeffizient \(\gamma\) /

The following formulas must be used to solve the exercise: \(V = V_0 \cdot (1+ 3\alpha \cdot \Delta\vartheta) \quad \) \(V = V_0 \cdot (1+ \gamma \cdot \Delta\vartheta) \quad \)

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No explanation / solution video for this exercise has yet been created.
But there is a video to a similar exercise:

In case your browser prevents YouTube embedding: https://youtu.be/gwOwzPOQY1E

Exercise:
The VzO steel aStO gas tank of a car is filled to the top with gasoline aGaO at TaO. The car sits in the sun and the tank reaches a temperature of TbO. How much gasoline do you expect to overflow from the tank? One US gallon is approximately .liter.

Solution:
At the new temperature the steel tank has SolQtydTTbX-TaXK SolQtyVTVX*+*aStX*dTXcubicmeter sscVT V_ +alpha Delta theta V + aSt dT VT Volume and the gasoline has SolQtyVGVX*+aGaX*dTXcubicmeter sscVG V_ +gammaDelta theta V +aGa dT VG We expect therefore SolQtydVVGX-VTXcubicmeter Delta V sscVG - sscVG VG - VT dV to overflow.

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Contained in these collections:

Volumenveränderung eines Glaskolbens by TeXercises

5 | 10
Ausdehnung von Flüssigkeiten by uz

6 | 10

Attributes & Decorations

Tags	extension, fluid, liquid, physics, thermodynamics
Content image
Difficulty	(3, default)
Points	3 (default)
Language	(English)
Type	Calculative / Quantity
Creator	uz
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