How Much Cold Water Is Needed to Adjust Bath Temperature?

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SUMMARY

To adjust the bath temperature from 60°C to 36°C by adding cold water at 9°C, a specific calculation using the principle of heat exchange is required. The equation mct=-mct can be applied, where m represents mass, c is specific heat capacity, and t is temperature change. The solution involves determining the mass of cold water needed as a fraction of the total tub volume to achieve the desired final temperature. This calculation is essential for accurately mixing hot and cold water in bath preparation.

PREREQUISITES
  • Understanding of heat transfer principles
  • Familiarity with the equation mct=-mct
  • Basic knowledge of temperature scales (Celsius)
  • Ability to perform algebraic manipulations
NEXT STEPS
  • Calculate the mass of cold water needed using the heat exchange equation
  • Explore specific heat capacity values for water
  • Learn about temperature conversion between Celsius and other scales
  • Investigate practical applications of heat transfer in everyday scenarios
USEFUL FOR

Students studying thermodynamics, individuals preparing baths, and anyone interested in practical applications of heat transfer principles.

Madeline1844
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MODERATOR NOTE: MISPLACED HOMEWORK, SO NO TEMPLATE

When filling up the tub for a bath, only the hot water tap was turned on. After realizing the mistake after a minute with half the tub at 60 C, how much cold water (as fraction of the whole tub) at 9 C must be added such that the final temperature of the water is 36 C?

Would the solution have to do with the equation mct=-mct?

Thanks in advance!
 
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Madeline1844 said:
Would the solution have to do with the equation mct=-mct?
If you fix the symbols there (are the mct on the left and right side the same thing?) and write down what they mean, you can use this formula, yes.
 

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