A piece of copper at 90°C is added 2.200 KG of water at 15°C inside an aluminum calorimeter that has a mass of .100 KG the final temperature of the copper water and calorimeter is 25°C what is the mass of the copper piece
heat lost by Cu + heat gained by Al + heat gained by water = 0
[mass Cu x specific heat Cu x (Tfinal-Tinitial)] + [mass Al x specific heat Al x (Tfinal-Tinitial)] + [mass H2O x specific heat H2O x (Tfinal-Tinitial)] = 0
I would convert all to grams and use specific heat in J/g*C
To find the mass of the copper piece, we can use the principle of conservation of energy.
The heat lost by the copper piece is equal to the heat gained by the water and the calorimeter.
The heat lost or gained by a substance depends on its mass, specific heat capacity, and the change in temperature. The specific heat capacity of copper is 0.385 J/g°C, and for water, it is 4.186 J/g°C. The specific heat capacity of aluminum is not provided, but we can assume it to be equal to the specific heat capacity of water for this calculation.
First, let's find the heat lost by the copper piece. We can use the formula:
Q = m * c * ΔT
where:
Q is the heat lost/gained (in Joules)
m is the mass (in grams)
c is the specific heat capacity (in J/g°C)
ΔT is the change in temperature (in °C)
The initial temperature of the copper is 90°C, and the final temperature is 25°C. The specific heat capacity of copper is 0.385 J/g°C.
Q_copper = m_copper * c_copper * ΔT_copper
Q_copper = m_copper * 0.385 * (25 - 90)
Similarly, the heat gained by the water and the calorimeter is given by:
Q_water+calorimeter = m_water+calorimeter * c_water * ΔT_water+calorimeter
Q_water+calorimeter = (m_water + m_calorimeter) * 4.186 * (25 - 15)
Since the total heat lost by the copper is equal to the total heat gained by the water and the calorimeter, we can set up the equation:
Q_copper = Q_water+calorimeter
m_copper * 0.385 * (25 - 90) = (m_water + m_calorimeter) * 4.186 * (25 - 15)
Simplifying the equation further:
m_copper * (25 - 90) = (m_water + m_calorimeter) * (4.186 * 10)
Now, substitute the given values:
m_water = 2200 g (mass of water)
m_calorimeter = 100 g (mass of calorimeter)
(25 - 90) * m_copper = (2200 + 100) * (4.186 * 10)
Solving for m_copper:
(m_copper * (-65)) = (2300) * (41.86)
m_copper = (2300 * 41.86) / (-65)
m_copper ≈ 1485.846 g
So, the mass of the copper piece is approximately 1485.846 grams.