How Does Mixing Coffee, Cream, and a Ceramic Cup Affect Temperature Equilibrium?

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SUMMARY

The discussion focuses on calculating the temperature equilibrium of a system involving a ceramic cup, coffee, and cream. The ceramic cup has a mass of 137 g and a specific heat capacity of 1090 J/(kgK). The coffee weighs 265 g at 80.3°C, while the cream weighs 12.2 g at 5.00°C. The equilibrium temperature can be determined using the principle of conservation of energy, specifically by applying the equation Q = mcΔT for each component and setting the heat gained equal to the heat lost.

PREREQUISITES
  • Understanding of specific heat capacity and its units (J/(kgK))
  • Knowledge of the conservation of energy principle in thermodynamics
  • Ability to perform calculations involving mass, temperature change, and heat transfer
  • Familiarity with the equation Q = mcΔT for heat transfer calculations
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  • Learn how to apply the conservation of energy principle in thermodynamic systems
  • Study specific heat capacities of various substances, particularly water
  • Explore detailed examples of heat transfer calculations involving multiple components
  • Investigate the effects of different materials on heat retention and transfer
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This discussion is beneficial for students in physics or chemistry, educators teaching thermodynamics, and anyone interested in practical applications of heat transfer principles.

map7s
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A ceramic coffee cup, with m = 137 g and c = 1090 J/(kgK), is initially at room temperature (24.0°C). If 265 g of 80.3°C coffee and 12.2 g of 5.00°C cream are added to the cup, what is the equilibrium temperature of the system? Assume that no heat is exchanged with the surroundings, and that the specific heat of coffee and cream are the same as the specific heat of water.

I tried to use the equation c=Q/(mdeltaT) but I'm not sure what to plug in for Q because I can't calculate its value. Am I completely off track about the equation?
 
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Ummm... Sort of. Try writing out the whole equation that relates increase in energy and decrease in energy.
 

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