The specific heat of copper metal was determined by putting a piece of the metal weighing 33.6 g in hot water. The quantity of heat absorbed by the metal was calculated to be 47 J from the temperature drop of the water. What was the specific heat of the metal if the temperature of the metal rose 3.63°C?

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To find the specific heat of copper metal, we can use the formula:

Q = mcΔT

Where:
Q = heat absorbed by the metal (47 J)
m = mass of the metal (33.6 g)
c = specific heat of the metal (unknown)
ΔT = change in temperature (3.63°C)

Let's plug in the given values and solve for c:

47 J = (33.6 g) * c * (3.63°C)

First, convert the mass of the metal to kilograms since the specific heat is usually expressed in J/g°C:

m = 33.6 g = 33.6 g * (1 kg / 1000 g) = 0.0336 kg

Now, rearrange the equation to solve for c:

c = 47 J / (0.0336 kg * 3.63°C)

c = 47 J / (0.121968 kg°C)

c ≈ 385.56 J/kg°C

Therefore, the specific heat of copper metal is approximately 385.56 J/kg°C.