Exercise
https://texercises.com/exercise/cooling-orange-juice-with-ice-cubes/
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The following quantities appear in the problem: Masse \(m\) / Temperatur \(T\) / Wärme \(Q\) / spezifische latente Wärme \(L\) / Wärmekapazität \(c\) /
The following formulas must be used to solve the exercise: \(Q = c \cdot m \cdot \Delta\vartheta \quad \) \(Q = m \cdot L_{\scriptscriptstyle\rm f} \quad \) \(\sum Q^\nearrow \stackrel{!}{=} \sum Q^\swarrow \quad \)
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Exercise:
If you add maO ice cubes at TaO to a large glass of orange juice mbO at a temperature of TbO -- to what final temperature will the juice be cooled in the best case scenario? The orange juice can be considered to a good approximation as water.

Solution:
% unknowntheta^* % WaermeSchritte PGleichungQnutz &mustbe Qzu PGleichungsscQO sscQE + ssctilde QEf + sscQE PGleichungssccW sscmO DeltasscthetaO ssccE sscmE DeltasscthetaE + sscmE sscLEf + ssccW sscmE DeltasscthetaE PGleichungssccW sscrhoW sscVO sscthetaO - uk ssccE sscmE sscthetaEf - sscthetaE + sscmE sscLEf + ssccW sscmE uk - sscthetaEf % AlgebraSchritte MGleichungssccW sscrhoW sscVO sscthetaO - ssccW sscrhoW sscVOuk ssccE sscmE sscthetaEf - sscthetaE + sscmE sscLEf + ssccW sscmE uk - ssccW sscmE sscthetaEf MGleichungssccW sscmE uk + ssccW sscrhoW sscVOuk ssccW sscrhoW sscVO sscthetaO + ssccW sscmE sscthetaEf - ssccE sscmE sscthetaEf - sscthetaE - sscmE sscLEf MGleichungssccW sscmE + sscrhoW sscVO uk ssccW sscrhoW sscVO sscthetaO + ssccW sscmE sscthetaEf - ssccE sscmE sscthetaEf - sscthetaE - sscmE sscLEf MGleichunguk fracssccW sscrhoW sscVO sscthetaO + ssccW sscmE sscthetaEf - ssccE sscmE sscthetaEf - sscthetaE - sscmE sscLEfssccW sscmE + sscrhoW sscVO % PHYSMATH % Die Mischtemperatur beträgt al theta^*
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Exercise:
If you add maO ice cubes at TaO to a large glass of orange juice mbO at a temperature of TbO -- to what final temperature will the juice be cooled in the best case scenario? The orange juice can be considered to a good approximation as water.

Solution:
% unknowntheta^* % WaermeSchritte PGleichungQnutz &mustbe Qzu PGleichungsscQO sscQE + ssctilde QEf + sscQE PGleichungssccW sscmO DeltasscthetaO ssccE sscmE DeltasscthetaE + sscmE sscLEf + ssccW sscmE DeltasscthetaE PGleichungssccW sscrhoW sscVO sscthetaO - uk ssccE sscmE sscthetaEf - sscthetaE + sscmE sscLEf + ssccW sscmE uk - sscthetaEf % AlgebraSchritte MGleichungssccW sscrhoW sscVO sscthetaO - ssccW sscrhoW sscVOuk ssccE sscmE sscthetaEf - sscthetaE + sscmE sscLEf + ssccW sscmE uk - ssccW sscmE sscthetaEf MGleichungssccW sscmE uk + ssccW sscrhoW sscVOuk ssccW sscrhoW sscVO sscthetaO + ssccW sscmE sscthetaEf - ssccE sscmE sscthetaEf - sscthetaE - sscmE sscLEf MGleichungssccW sscmE + sscrhoW sscVO uk ssccW sscrhoW sscVO sscthetaO + ssccW sscmE sscthetaEf - ssccE sscmE sscthetaEf - sscthetaE - sscmE sscLEf MGleichunguk fracssccW sscrhoW sscVO sscthetaO + ssccW sscmE sscthetaEf - ssccE sscmE sscthetaEf - sscthetaE - sscmE sscLEfssccW sscmE + sscrhoW sscVO % PHYSMATH % Die Mischtemperatur beträgt al theta^*
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Asked Quantity
Tags
eis, kalorik, physik, schmelzwärme, temperatur, thermodynamik, wasser, wärmekapazität
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(4, default)
Points
3 (default)
Language
ENG (English)
Type
Calculative / Quantity
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