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?
13.9
To find the heat capacity of the copper in joules per kelvin (J/K), you can use the equation:
Q = m * c * ΔT
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 is initially at 100 °C and reaches a final temperature of 25 °C. So the change in temperature, ΔT, is:
ΔT = final temperature - initial temperature
= 25 °C - 100 °C
= -75 °C
Now you need to determine the mass of the copper. The problem statement does not provide the mass of the copper, so you'll have to assume a certain mass. Let's say the mass of the copper is "m_c".
Using the same equation, Q = m * c * ΔT, you can rearrange it to solve for the mass of the copper:
m_c = Q / (c * ΔT)
Plugging in the known values:
m_c = Q / (4.18 J/(gK) * -75 °C)
The heat transfer, Q, is the same for both the copper and water because they reach the same final temperature. The heat transfer can be determined using:
Q = m_water * c_water * ΔT_water
Where m_water is the mass of the water and c_water is the specific heat capacity of water.
Given:
m_water = 50.0 g
c_water = 4.18 J/(gK)
ΔT_water = final temperature - initial temperature = 25 °C - 20 °C = 5 °C
Plugging in these values:
Q = (50.0 g) * (4.18 J/(gK)) * (5 °C)
Now that you have the value for Q, you can substitute it back into the equation for the mass of the copper:
m_c = [(50.0 g) * (4.18 J/(gK)) * (5 °C)] / (4.18 J/(gK) * -75 °C)
The units for mass will cancel out, leaving you with:
m_c = (50.0 g) * (5 °C) / -75 °C
Now you can calculate the value of m_c, which represents the mass of the copper.
Once you have determined the mass of the copper, you can calculate the heat capacity, C_c, using the formula:
C_c = m_c * c_copper
Where c_copper is the specific heat capacity of copper.
Unfortunately, the problem statement does not provide the value for the specific heat capacity of copper, so you will need to look up this value. The specific heat capacity of copper is approximately 0.39 J/(gK).
Finally, multiply the mass of the copper by the specific heat capacity of copper to find the heat capacity of the copper in J/K:
C_c = (mass of copper) * (specific heat capacity of copper)