What is the final temperature after a 11.9 g piece of ice is placed into a Styrofoam cup containing 110 g of hot water at 73.3 degrees Celsius?

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To find the final temperature, we can use the principle of conservation of energy, which states that the energy lost by the hot water is equal to the energy gained by the ice.

We can use the equation:

(mass of water) × (specific heat capacity of water) × (change in temperature of water) = (mass of ice) × (specific heat capacity of ice) × (change in temperature of ice)

First, let's find the initial and final temperatures of the water.

The initial temperature of the water is given as 73.3 degrees Celsius.

The final temperature will be the same for both the water and the ice, so let's call it "T."

Using the equation, let's calculate the change in temperature for the water:

(110 g) × (specific heat capacity of water) × (T - 73.3) = 0

Now, let's find the specific heat capacity of water and ice.

The specific heat capacity of water is approximately 4.184 J/g°C.

The specific heat capacity of ice is approximately 2.09 J/g°C.

Now, let's substitute the values into the equation:

(110 g) × (4.184 J/g°C) × (T - 73.3) = (11.9 g) × (2.09 J/g°C) × (T - 0)

Simplifying the equation:

(459.24 J/°C) × (T - 73.3) = (24.871 J/°C) × T

Expanding and rearranging the equation:

459.24 T - 33611.652 = 24.871 T

Combining like terms:

434.369 T = 33611.652

Solving for T:

T ≈ 77.41 degrees Celsius

Therefore, the final temperature of the water and the ice will be approximately 77.41 degrees Celsius.