183_notes:examples:thermal_equilibrium

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183_notes:examples:thermal_equilibrium [2014/10/28 05:02] – created pwirving183_notes:examples:thermal_equilibrium [2014/10/28 13:54] (current) – pwirving
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 Final State: Blocks have come to thermal equilibrium, same $T_{f}$ Final State: Blocks have come to thermal equilibrium, same $T_{f}$
  
 +300 gram block of aluminum which is at a temperature of 500 K
  
-=== Lacking ===+650 gram block of iron which is at a temperature of 350 K
  
 +Aluminum is placed on iron
  
 +Both in insulated enclosure
 +
 +Specific heat capacity of aluminum is approximately 1.0 J/K/gram
 +
 +Specific heat capacity of iron is approximately 0.42 J/K/gram
 +
 +Metal blocks reach same temperature 
 +
 +
 +=== Lacking ===
 +
 +$T_{f}$ common temperature 
  
 === Approximations & Assumptions === === Approximations & Assumptions ===
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 The total energy of the two blocks does not change, because there is no energy transfer from or to the surroundings. The total energy of the two blocks does not change, because there is no energy transfer from or to the surroundings.
 +
 +Therefore we want to solve for $T_{f}$ which is the final temperature for both blocks.
  
 $m_{1}C_{1}(T_{f} - T_{1i}) + m_{2}C_{2}(T_{f} - T_{2i}) = 0$ $m_{1}C_{1}(T_{f} - T_{1i}) + m_{2}C_{2}(T_{f} - T_{2i}) = 0$
 +
 +Substitute in values for all known variables and solve for $T_{f}$.
  
 $(300g)(1.0 J/K/g)(T_{f} - 500) + (650 g)(0.42 J/K/g)(T_{f} - 350) = 0$ $(300g)(1.0 J/K/g)(T_{f} - 500) + (650 g)(0.42 J/K/g)(T_{f} - 350) = 0$
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