You drop a hot copper penny (500 degrees celsius) that has a mass of 4.5 grams into a glass of cold water (6.0 degrees celsius) with a volume of 120 mL. The water heats up to 7.7 degrees celsius. Find the heat absorbed by the water, then determine the specific heat of copper. Give your answer in correct sig figs.
q1 = heat absorbed by water = mass H2O x specific heat H2O x delta T.
For part 2, I believe it's best to do it all in one.
heat lost by Cu + heat gained by water = 0
heat lost by Cu = mass Cu x specific heat Cu x delta T.
heat gained by water = done in part 1.
one unknown, specific heat Cu. Solve for that. Post your work if you need additional help.
To find the heat absorbed by the water, you can use the formula:
Q = m * c * ΔT
Where:
Q is the heat absorbed by the water (in joules)
m is the mass of the water (in grams)
c is the specific heat capacity of water (in J/g°C)
ΔT is the change in temperature of the water (in °C)
First, convert the given values:
mass of the water (m) = 120 mL = 120 grams (since the density of water is 1 g/mL)
initial temperature (6.0 °C)
final temperature (7.7 °C)
change in temperature (ΔT) = final temperature - initial temperature = 7.7 °C - 6.0 °C = 1.7 °C
Now, substitute the values into the formula:
Q = 120 g * c * 1.7 °C
To find the specific heat capacity of copper, you can use the formula:
Q = m * c * ΔT
Where:
Q is the heat absorbed by the copper (in joules)
m is the mass of the copper (in grams)
c is the specific heat capacity of copper (in J/g°C)
ΔT is the change in temperature of the copper (in °C)
The heat absorbed by the copper is equal to the heat absorbed by the water. So we can set up the equation:
Q of water = Q of copper
120 g * c_water * 1.7 °C = 4.5 g * c_copper * 1.7 °C
Since we want to find the specific heat capacity of copper, rearrange the equation:
c_copper = (120 g * c_water * 1.7 °C) / (4.5 g * 1.7 °C)
Now, substitute the specific heat capacity of water, which is approximately 4.18 J/g°C:
c_copper = (120 g * 4.18 J/g°C * 1.7 °C) / (4.5 g * 1.7 °C)
Simplifying the expression:
c_copper ≈ (120 * 4.18) / 4.5 J/g
c_copper ≈ 111.47 J/g.
Therefore, the specific heat capacity of copper is approximately 111.5 J/g°C (rounded to the correct number of significant figures).