What Went Wrong in Calculating Equilibrium Temperature?

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SUMMARY

The discussion centers on calculating the equilibrium temperature of a system involving a lead ball and water using the equation Q = mc ΔT. The user initially misapplied the specific heat capacities by using the specific heat of water (4.186 J/g°C) for the lead ball and the specific heat of lead incorrectly as 0.13 J/g°C. The correct equilibrium temperature calculated is 82.5°C after addressing the errors in specific heat values and the sign in the equation.

PREREQUISITES
  • Understanding of thermodynamics principles, specifically heat transfer.
  • Familiarity with the equation Q = mc ΔT for calculating heat exchange.
  • Knowledge of specific heat capacities of materials, particularly water and lead.
  • Basic algebra skills for solving equations.
NEXT STEPS
  • Research the specific heat capacity of lead to confirm accurate values.
  • Learn more about calorimetry and its applications in thermal physics.
  • Explore common mistakes in heat transfer calculations and how to avoid them.
  • Study the concept of thermal equilibrium and its significance in physical chemistry.
USEFUL FOR

Students studying thermodynamics, educators teaching calorimetry, and anyone interested in understanding heat transfer calculations in physical systems.

mikep
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A 199 g lead ball at a temperature of 80.9°C is placed in a light calorimeter containing 178 g of water at 24.5°C. Find the equilibrium temperature of the system.

i used the equation [tex]Q = mc \Delta T[/tex]
-(199g)(4.186J/g°C)(T - 80.9°C) + (178g)(0.13J/g°C)(T - 24.5°C) = 0
T = T final = 82.5°C
can someone please tell mw what i did wrong?
can someone also confirm if the specific heat for lead is 0.13J/g°C?
 
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mikep said:
can someone please tell mw what i did wrong?

You put the specific heat of water in the term for the lead ball, and vice versa.

can someone also confirm if the specific heat for lead is 0.13J/g°C?

Not off the top of my head, but if you type "specific heat lead" into Google, I'm sure you can find it.
 
oh yeah and i also didn't need the negative sign. i got it thanks
 

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