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A 99.1 g piece of copper (specific heat 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 a final temperature of 22.2 °C. What is the

initial temperature (in °C) of the copper? (The specific heat of water is

4.184 J/g °C).

A 99 1 g piece of copper specific heat 0 380 J g C is heated and then placed into 400 0 g of water

Answer :

The initial temperature of the copper can be calculated using the principle of energy conservation. When the copper is heated and then placed in the water, the heat gained by the copper equals the heat lost by the water.

Using the formula for heat transfer, we find that the initial temperature of the copper is approximately 41.93°C. This means that the copper was initially heated to around 41.93°C before being placed in the 400.0 g of water at 20.7°C, which led to a final equilibrium temperature of 22.2°C for the water.

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Rewritten by : Barada

The initial temperature of the copper is 89.8°C.

To find the initial temperature of the copper, we apply the principle of conservation of energy, where heat lost by the copper equals heat gained by the water.

Given data:

Mass of copper, mCu = 99.1 g

Specific heat of copper, cCu = 0.380 J/g°C

Mass of water, mH2O = 400.0 g

Specific heat of water, cH2O = 4.184 J/g°C

Initial temperature of water, Tinitial, H2O = 20.7°C

Final temperature of the system, Tfinal = 22.2°C

Step-by-step solution:

Calculate the heat gained by the water:

QH2O = mH2O x cH2O x (Tfinal - Tinitial, H2O) = 400.0 g x 4.184 J/g°C x (22.2°C - 20.7°C) = 2508 J

Apply the conservation of energy principle, setting the heat lost by the copper equal to the heat gained by the water:

QCu = QH2O

Calculate the initial temperature of the copper using the formula:

QCu = mCu x cCu x (Tinitial, Cu - Tfinal)

2508 J = 99.1 g x 0.380 J/g°C x (Tinitial, Cu - 22.2°C)

2508 J = 37.258 J/°C x (Tinitial, Cu - 22.2°C)

Solve for Tinitial, Cu:

Tinitial, Cu = (2508 J / 37.258 J/°C) + 22.2°C = 89.8°C

Therefore, the initial temperature of the copper piece is 89.8°C.