Final answer:
To find the specific heat of an unknown metal when mixed with water, heat transfer principles were used. The heat gained by water was calculated and set equal to the heat lost by the metal. The specific heat of the metal was calculated to be 0.836 J/g°C, which does not match the provided options.
Step-by-step explanation:
The student's question involves determining the specific heat of an unknown metal by using a heat transfer equation. According to the principle of conservation of energy, the heat lost by the metal will be equal to the heat gained by the water. The formula to calculate the change in thermal energy (ΔQ) is:
ΔQ = m × c × ΔT
where m is mass, c is specific heat capacity, and ΔT is the change in temperature. For the water in this scenario, we know that m = 200 g, c = 4.18 J/g°C, and ΔT = (25.0°C - 22.0°C) = 3.0°C.
The unknown metal has m = 40.0 g, and ΔT = (25.0°C - 100°C) = -75.0°C (negative because the metal is cooling down).
First, calculate the energy change for water:
ΔQ_water = 200 g × 4.18 J/g°C × 3.0°C = 2508 J
The metal loses the same amount of energy as the water gains, so:
ΔQ_metal = ΔQ_water = 2508 J
To find the specific heat (c_metal), rearrange the equation to solve for c:
c_metal = ΔQ_metal / (m × ΔT)
c_metal = 2508 J / (40.0 g × -75.0°C)
c_metal = 2508 J / -3000 g°C
c_metal = -0.836 J/g°C
The negative sign indicates the direction of heat flow (out of the metal), so we take the magnitude of the value for the purpose of specific heat. Therefore, the specific heat of the unknown metal is 0.836 J/g°C. This does not match any options (A, B, C, D), indicating a likelihood of either an error in calculations or a mistake in the provided options.