To determine the specific heat of the unknown metal, we can use the principle of heat transfer between the metal and water. The formula for heat transfer is:
Q = m * c * ΔT
Where: Q is the heat transfer (in Joules), m is the mass of the substance (in grams), c is the specific heat capacity (in J/g°C), ΔT is the temperature change (in °C).
In this case, the heat transfer from the metal to the water can be calculated using the initial and final temperatures of the water. Since we know the mass of the metal and the temperature changes of the water, we can solve for the specific heat capacity of the metal.
First, let's calculate the heat transfer from the metal to the water:
Q = m * c * ΔT
The mass of the metal is given as 4.82 grams, and the temperature change of the water is:
ΔT = final temperature - initial temperature ΔT = 34.5°C - 28.7°C ΔT = 5.8°C
Now, we need to determine the heat transfer (Q) from the metal to the water. We can use the heat transfer equation:
Q = m_water * c_water * ΔT_water
Where: m_water is the mass of the water c_water is the specific heat capacity of water (4.18 J/g°C) ΔT_water is the temperature change of the water
The mass of water is given as 35 mL, which is equivalent to 35 grams.
Now we can set up the equation:
Q = (mass of water) * c_water * ΔT_water = m_metal * c_metal * ΔT_metal
Substituting the given values:
35 g * 4.18 J/g°C * 5.8°C = 4.82 g * c_metal * 5.8°C
Simplifying:
c_metal = (35 g * 4.18 J/g°C * 5.8°C) / (4.82 g * 5.8°C)
c_metal ≈ 20.54 J/g°C
Therefore, the specific heat of the unknown metal is approximately 20.54 J/g°C.