Final answer:
To calculate the heat transferred to the aluminum piece, use the equation q = m * c * ΔT. Substitute the given values to find the initial temperature of the aluminum and then calculate q. The heat transferred to the aluminum is approximately 2093.5 J.
Step-by-step explanation:
To calculate the heat (q) transferred to the aluminum piece, we can use the equation:
q = m * c * ΔT
where:
m is the mass of the aluminum piece,
c is the specific heat of aluminum,
ΔT is the change in temperature.
In this case, the mass of the aluminum is 50.0 g, the specific heat of aluminum is 900 J/kg°C, and the change in temperature is the final temperature of the water (40.0°C) minus the initial temperature of the aluminum (which we need to calculate).
Let's assume the initial temperature of the aluminum is T.
The heat transferred to the water can be calculated using the equation:
q = m * c * ΔT
where:
m is the mass of the water,
c is the specific heat of water,
ΔT is the change in temperature. In this case, the mass of the water is 50.0 g, the specific heat of water is 4.184 J/g°C, and the change in temperature is the final temperature of the water (40.0°C) minus the initial temperature of the water (which was not provided in the question).
To find the initial temperature of the aluminum, we can set up the equation:
q_aluminum = q_water
m_aluminum * c_aluminum * ΔT_aluminum = m_water * c_water * ΔT_water
Substituting the given values, we have:
(50.0 g) * (900 J/kg°C) * (T - 40.0°C) = (50.0 g) * (4.184 J/g°C) * (40.0°C - T)
Simplifying the equation,
45000(T - 40.0°C) = 20920(40.0°C - T)
Solving for T, we find:
T ≈ 59.93°C
Substituting this value into the equation to calculate the heat transferred to the aluminum, we have:
q = (50.0 g) * (900 J/kg°C) * (59.93°C - 40.0°C)
Simplifying,
q ≈ 2093.5 J
Therefore, the heat (q) in joules of the piece of aluminum metal is approximately 2093.5 J, option a).