A hot, just-minted copper coin is placed in 109 g of water to cool. The water temperature changes by 8.93◦C and the temperature of the. . .
coin changes by 89.4◦C.
What is the mass of the coin? Disregard any energy transfer to the water’s surround- ings and assume the specific heat of copper is 387 J/kg ·◦ C. The specific heat of water is 4186 J/kg ·◦ C .
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The specific heat is the measure of how much heat per unit mass required to raise the temperature by 1º Celsius. The formula is given as
Q = cm∆T where
Q = the amount of heat added
c = specific heat of a substance
∆T = change in temperature in ºC, or (T final - T initial)
Since it's not given, I'm assuming the initial temperature of the water is 0ºC, in keeping with good chemical practice of Standard Temperature and Pressure (STP.) If so, then the change in the amount of heat to the water is:
Q = (4186 J/kg ºC) * (.109 Kg) * (8.93 - 0 ºC) = 4074.53 J
So 4074.53 Joules of heat went into the water, which we will assume all originated from the hot copper coin, which lost that exact amount of heat. So the change in the amount of heat to the copper coin is:
4074.53 J = (387 J/kg ºC) * (Cu mass) * (89.4 - 0 ºC)
If we rearrange terms, we can solve for the mass of the copper:
4074.53 J / (387 J/kg ºC) * (89.4 - 0 ºC) = Cu mass
4074.53 J / 34597.8 J/kg = Cu mass
.11777 kg = 117.77 g = Cu mass
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