Answer :
Final answer:
The initial temperature of the copper piece is approximately 0.72°C.
Explanation:
To find the initial temperature of the copper piece, we can use the equation Q = mcΔT, where Q is the heat energy, m is the mass of the substance, c is the specific heat capacity, and ΔT is the change in temperature.
First, let's calculate the heat energy gained by the water. The mass of the water is 400.0 g, and the change in temperature is 22.2°C - 20.7°C = 1.5°C.
Using the equation Q = mcΔT, we have:
Q_water = (400.0 g)(4.18 J/g • °C)(1.5°C) = 2490 J
Next, let's calculate the heat energy lost by the copper piece. The mass of the copper is 90.7 g, and the change in temperature is the same as the water, 1.5°C.
Using the equation Q = mcΔT, we have:
Q_copper = (90.7 g)(0.380 J/g • °C)(1.5°C) = 51.8 J
Since energy is conserved, the heat energy gained by the water is equal to the heat energy lost by the copper piece:
Q_water = Q_copper
2490 J = 51.8 J
Now, let's solve for the initial temperature of the copper piece. Rearranging the equation Q = mcΔT to solve for the initial temperature, we have:
T_initial = (Q_copper) / (m_copper * c_copper)
Substituting the values, we get:
T_initial = (51.8 J) / (90.7 g * 0.380 J/g • °C) ≈ 0.72°C
Therefore, the initial temperature of the copper piece is approximately 0.72°C.
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The initial temperature of copper is 89.41°C.
How to calculate temperature?
Calorimetry is the science of measuring the heat absorbed or evolved during the course of a chemical reaction or change of state.
According to this question, a 98.3 g piece of copper with specific heat of 0.380 J/g･°C is heated and then placed into 400.0 g of water initially at 20.7°C. The water increases in temperature to 22.2°C. The initial temperature can be calculated as follows;
Q = mc∆T
Where;
- Q = quantity of energy
- m = mass of substance
- c = specific heat capacity
- ∆T = change in temperature
Q(water) = -Q(metal)
400 × 4.184 × 1.5 = -(98.3 × 0.38 × {22.2 - x})
2510.4 = - (829.26 - 37.354x)
2510.4 = -829.26 + 37.354x
3339.659 = 37.354x
X = 89.41°C
Therefore, 89.41°C is the initial temperature of the copper metal.
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