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?

A hint here, then read Ms. Sue's response above.

heat gained by metal = q
heat gained by metal is mass x specific heat metal x delta T. You know q, mass and delta T. That leaves only one unknown.

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

q = m * c * ΔT

Where:
q is the quantity of heat absorbed by the metal (in joules)
m is the mass of the metal (in grams)
c is the specific heat of the metal (in J/g°C)
ΔT is the change in temperature of the metal (in °C)

We know:
q = 47 J
m = 33.6 g
ΔT = 3.63°C

Plugging in the given values into the formula, we can solve for c:

47 J = 33.6 g * c * 3.63°C

To isolate c, we divide both sides of the equation by (33.6 g * 3.63°C):

47 J / (33.6 g * 3.63°C) = c

Calculating the result gives us the specific heat of the metal:

c = 0.401 J/g°C

Therefore, the specific heat of the copper metal is 0.401 J/g°C.