What Is the Initial Temperature of Copper in a Mixed Substance System?

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SUMMARY

The discussion focuses on calculating the initial temperature of copper in a thermal equilibrium problem involving aluminum and ethyl alcohol. The user attempted to apply the heat transfer equation Q=McΔT but encountered difficulties in determining the correct initial temperature for copper. The final temperature of the system is established at 22°C, with aluminum at 200°C and ethyl alcohol at 15°C. The user correctly identified the need to balance heat lost and gained but struggled with the setup of the equation, leading to an incorrect initial temperature calculation of -130°C.

PREREQUISITES
  • Understanding of the heat transfer equation Q=McΔT
  • Knowledge of specific heat capacities for aluminum, copper, and ethyl alcohol
  • Ability to convert units, particularly mass from grams to kilograms
  • Familiarity with the concept of thermal equilibrium in mixed substance systems
NEXT STEPS
  • Review the principles of thermal equilibrium and heat transfer calculations
  • Study the specific heat capacities of aluminum, copper, and ethyl alcohol
  • Practice unit conversions, especially for mass and volume in thermal problems
  • Explore examples of mixed substance systems to reinforce understanding of heat exchange
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Students studying thermodynamics, physics educators, and anyone solving heat transfer problems in mixed substance systems.

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Homework Statement



What is the initial temperature of copper if, 11 g aluminum at 200 C and 21 g of copper are dropped into 46 cm^3 of ethyl alcohol at 15 C. The final temperature of the system is 22 C.




Homework Equations



Q=McT

The Attempt at a Solution



My work : Qal+Qcu+Qea=0, and solved for the intial temperature. I got -130 C which was wrong. To find the mass of ethyl alcohol, i used volume and density. Volume is 790 kg/m^3
 
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Try converting everything into the same units (eg kg)
 


i converted everything and got this formula

m1 * s1 * t1 + m2 * s2 * t2 + = m1 * s1 * tf + m2 * s2 * tf + m3 * s3 * tf

m1= aluminum
m2=coppper
m3=ethtyl alcohol,

i just can't get the write answer.
 


In Q=mcT , 'T' is the change in temperature
 


yea, i took that into account, so i did heat loss=heat gained, and the heat lost was by the aluminum, and i know the ethyl alcohol gained heat, but I am not sure what side the copper would go on
 


Al goes from 200 to 22
Cu goes from T to 22
Ethyl goes from 15 to 22

So
m_al * c_al * (200-22) + m_cu * c_cu * ( T-22) + m_eth * c_eth * (15-22) = 0
 

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