A piece of copper metal is initially at 100 C. It is dropped into a coffee cup calorimeter containing 50.0 g of water at a temperature of 20 C. After stirring, the final temperature of both copper and water is 25 C Assuming no heat losses, and that the specific heat (capacity) of water is 4.18 J (gK), what is the heat capacity of the copper in J/K?
I worked this earlier. If you can't find it I will look for a link.
To find the heat capacity of the copper in joules per kelvin (J/K), we can use the principle of energy conservation and the formula for heat transfer:
heat gained by the water = heat lost by the copper
The formula for heat transfer is:
Q = mcΔT
where Q is the heat transferred, m is the mass of the substance, c is the specific heat capacity, and ΔT is the change in temperature.
In this case, the copper loses heat, so we'll use a negative sign for its heat transfer:
Q_copper = -Q_water
First, let's calculate the heat transferred by the water:
Q_water = mcΔT
Q_water = (50.0 g)(4.18 J/(gK))(25 - 20) K
Q_water = (50.0 g)(4.18 J/(gK))(5) K
Q_water = 1045 J
Now, using the fact that the copper loses the same amount of heat:
Q_copper = -1045 J
To find the heat capacity of the copper, we divide the heat transfer by the change in temperature:
heat capacity of copper = Q_copper / ΔT
heat capacity of copper = -1045 J / (25 - 100) K
heat capacity of copper = -1045 J / (-75) K
heat capacity of copper = 13.93 J/K
Therefore, the heat capacity of the copper is approximately 13.93 J/K.