Heating Mineral Water to 60°C Using Plain Water at 100°C

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SUMMARY

The discussion centers on the challenge of heating 1 kg of mineral water from 0°C to 60°C using 1 kg of plain water at 100°C. The key equation used is \(\Delta Q = mc\Delta T\), which relates the heat gained by the mineral water to the heat lost by the plain water. The initial calculations indicate that the mass of the plain water required exceeds 1 kg, suggesting that a different approach or consideration of specific heat capacities is necessary. Participants emphasize the importance of recognizing the differences in specific heat capacities between mineral water and plain water.

PREREQUISITES
  • Understanding of thermodynamics principles, specifically heat transfer.
  • Familiarity with the specific heat capacity formula, \(\Delta Q = mc\Delta T\).
  • Knowledge of the specific heat capacities of water and mineral water.
  • Basic algebra skills for solving equations.
NEXT STEPS
  • Research the specific heat capacity of various types of mineral water.
  • Learn about heat transfer methods in thermodynamics.
  • Explore the concept of thermal equilibrium and its applications.
  • Investigate alternative methods for heating water, such as using heat exchangers.
USEFUL FOR

Students in physics or chemistry, educators teaching thermodynamics, and anyone interested in practical applications of heat transfer principles.

dogcat
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Homework Statement



How can you heat 1 \,\mathrm{kg} mineral water which is at a temperature of 0 \,{}^\circ \mathrm{C} to at least 60 \,{}^\circ \mathrm{C} with using 1 \,\mathrm{kg} plain water at a temperature of 100 \,{}^\circ \mathrm{C}?

Homework Equations



\Delta Q = mc\Delta T

The Attempt at a Solution


\underbrace{(1000 g)(4.18~J/g~C)(60~C)}_{\text{heat gained}} = \underbrace{m(4.18~J/g~C)(100~C - 60~C)}_{\text{heat lost}}
But then m>1000 g. So I really don't know how to do it. There should be a nasty trick in it.
 
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Check your cp's. They should be different given the temperature difference and though subtle, material difference.
 
Thanks but don't think that there are so much difference between them. Any other ideas?
 

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