Höhe von Aluminium-Kegel
Question
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The following quantities appear in the problem:
Masse \(m\) / Volumen \(V\) / Höhe \(h\) / molare Masse \(M\) / Stoffmenge \(n\) / Radius \(r\) / Dichte \(\varrho\) /
The following formulas must be used to solve the exercise:
\(\varrho = \dfrac{m}{V} \quad \) \(V = \dfrac{1}{3}\pi r^2 h \quad \) \(m = nM \quad \)
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Exercise:
Welche Höhe hätte ein aus nO Aluminium-Atomen gebauter Kegel mit raO Radius? Aluminium hat MO molare Masse und rO Dichte.
Solution:
Geg N nO rightarrow n n r raO ra textAluminium rightarrow M MO M textAluminium rightarrow rho rO r GesHöhehsim Der Aluminium-Kegel hat m nM n M m Masse und damit V fracmrho fracnMrho fracmr V Volumen. Er wäre also h fracVpi r^ fracfracnMrhopi r^ fracnMpi rho r^ fracVpi qtyr^ h hoch. h fracnMpi rho r^ h
Welche Höhe hätte ein aus nO Aluminium-Atomen gebauter Kegel mit raO Radius? Aluminium hat MO molare Masse und rO Dichte.
Solution:
Geg N nO rightarrow n n r raO ra textAluminium rightarrow M MO M textAluminium rightarrow rho rO r GesHöhehsim Der Aluminium-Kegel hat m nM n M m Masse und damit V fracmrho fracnMrho fracmr V Volumen. Er wäre also h fracVpi r^ fracfracnMrhopi r^ fracnMpi rho r^ fracVpi qtyr^ h hoch. h fracnMpi rho r^ h