Final answer:
To calculate the specific heat of the metal, use the heat transfer formula and the given values: q = 3,135 J, m = 63.0 g, and ΔT = 362°C. Solving for the specific heat capacity, c is determined to be 0.138 J/g°C.
Step-by-step explanation:
To determine the specific heat of the metal, we can use the formula:
q = m × c × ΔT
where:
- q is the heat absorbed or released (in joules),
- m is the mass of the substance (in grams),
- c is the specific heat capacity (in J/g°C), and
- ΔT is the change in temperature (in °C).
The question states that the metal has released 3,135 J of energy as it cooled down, which is the same amount of energy absorbed by the water. We're given that the mass (m) of the metal is 63.0 g and the temperature change (ΔT) is from 382°C to 20.0°C, thus ΔT is 382 - 20 = 362°C.
Plugging these values into the formula, we have:
3,135 J = 63.0 g × c × 362°C
To find c, the specific heat, rearrange the formula:
c = 3,135 J / (63.0 g × 362°C)
c = 0.138 J/g°C
So, the specific heat capacity of the metal is 0.138 J/g°C.