11.583 g of metal are heated to 99.8 degrees Celsius. This is poured into a calorimeter containing 25.118 g of H₂O at 24.7 degrees Celsius. The final temperature of the water and metal is 28.5 degrees Celsius. What is the specific heat of the metal?

A. 0.874 J/g°C
B. 0.988 J/g°C
C. 0.732 J/g°C
D. 1.165 J/g°C

The specific heat of the metal is calculated using the principle of heat conservation. Following the formula for heat transfer and solving it, the specific heat of the metal namely copper is found to be approximately 0.390 J/g °C.

Explanation:

To calculate the specific heat of the metal, we use the principle of conservation of energy, which states that the heat lost by the metal equals the heat gained by the water. The formula for this principle is:

Cmetal × mmetal × (Tinitial,metal – Tfinal) = Cwater × mwater × (Tfinal - Tinitial,water)

where:

C is the specific heat,
m is the mass,
Tinitial is the initial temperature, and
Tfinal is the final temperature.

Setting the known values and solving for the specific heat of the metal gives:

(Cmetal)(11.583 g)(99.8 °C – 28.5 °C) = (4.184 J/g °C)(25.118 g)(28.5 °C – 24.7 °C)

After solving the equation, we find the specific heat of the metal to be approximately 0.390 J/g °C.

Our experimental specific heat is closest to the specific heat of copper, which means the metal in this scenario is probably copper.

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