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What is the Final temperature inside the calorimeter?
One Piece of Copper jewelry at 119°C has exactly twice the mass of another piece, which is at 53.0°C. Both Pieces are placed inside a calorimeter whose Heat Capacity is negligible. What is the final temperature inside the calorimeter (s of copper = 0.387 J/gK)?
I have no idea where to Start, if someone could just help me with the equation and the answer I'd really appreciate it!
dH = m C dT
since both are copper... if they had the same mass and you Mixed them the final Temp would be Half Way in between. one would go up in temp absorbing the Joules lost by the hotter one , as equally as the hotter one would go Down in temp as it loses energy.
there is 66 degrees Celsius between them
However the heavier piece has twice the mass.
when it drops one degree, it releases enough heat to raise the temp of the Other by Two degrees Celsius.
With a 66 degree spread at the start, they are in essence moving in thirds. the heavier one comes down 1/3 of the 66 degrees, while the other goes up twice that (2/3 of the 66 degrees).
they will meet 2/3 the way through the 66 degree spread. the twice as massive one will Come down by 22 degrees Celsius to 97 Celsius, while the lighter one will Rise by 44 degrees celsius to meet the other @ 97 celsius
97 celsius
----------------
with a formula huh..... ok
lets say that the lighter one weighs "X", which Make the heavier one "2X"
first one calculates the excess energy that the heavier one has because it is hotter by 66 degrees
dH = m C dT = (2X) (0.387) (66) = 51.08X joules
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then you say when you Take this excess energy away Form the heavier one, it would cool to the same temp as the lighter one. then if you were to re-instate these 51.08X joules they would heat both pieces, (the X & the 2X), to the temp that they would have equilibated to if we had Left them alone. So:
dH = m C dT
51.08X Joules = (3X) (0.387)(dT)
dT = 44 degree rise in temp From 53 celsius
so they would rise to 97Celsius
