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Eisenkugel

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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

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Level 5 -
Level 6 -

Exercise

https://texercises.com/exercise/eisenkugel/

Question

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

The following formulas must be used to solve the exercise: \(V = \dfrac{4}{3}\pi r^3 \quad \) \(V = V_0 \cdot (1+ 3\alpha \cdot \Delta\vartheta) \quad \)

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Exercise:
Eine Eisenkugel Formelbuchper-modereciprocal.perkelvin habe bei degreeCelsius einen Durchmesser von .mm. abcliste abc Auf welche Temperatur ist sie zu erhitzen damit sie in einem kreisrunden Loch mit .mm Öffnung gerade stecken bleibt? abc Um welchen Betrag hat sich dabei das Kugelvolumen vergrössert? abcliste

Solution:
pmrec newqtya.perkelvin newqtydo.m newqtyd.m % Geg textEisenkugeltoalpha a d_ .mm do d .mm d % abclist abc GesTemperaturdifferenzDeltatheta sicelsius % Wir berechnen zunächst das Volumen das die Kugel bei celsius hat und jenes das sie nach dem Erhitzen mindestens haben muss: solqtyVfracpi d^/*pi*dn**cubicmeter solqtyVofracpi d_^/*pi*don**cubicmeter al V_ Vof fracpi qtydo^ Vo V Vf fracpi qtyd^ V. Wir lösen die Formel für die Volumenausdehnung nach Deltatheta auf: al V V_ + V_alphaDeltatheta V - V_ V_ alpha Deltatheta fracVV_-fracV-V_V_ alpha Deltatheta Deltatheta fracalphaqtyfracVV_ - Daraus können wir die Temperaturdifferenz die in diesem Fall der neuen Temperatur entspricht berechnen: solqtyDTfracalpha qtyfracd^d_^-Vn-Von/*an*Voncelsius al Deltatheta fracalphaqtyfracVV_ - DTf fracV - Voa TecDT. % Deltatheta DTf TecDT abc GesVolumendifferenzDelta V sicubicmeter % Die Volumifferenz beträgt solqtyDVfracpid^-d_^Vn-Voncubicmeter solqtyDVmmDVn*ecubicmillimeter al Delta V V-V_ DVf V - Vo DV. % Delta V DVf TecDVmm abclist pmfrac

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Contained in these collections:

Thermische Ausdehnung von Volumina by TeXercises

1 | 7
Längenänderung von Festkörpern by pw

9 | 12

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Tags	ausdehnung, eisen, festkörper, physik, tabellenwerk, wärmelehre
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Difficulty	(3, default)
Points	2 (default)
Language	(Deutsch)
Type	Calculative / Quantity
Creator	uz
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