Final answer:
The specific heat of lead is 0.031 J/(g°C).
Step-by-step explanation:
The specific heat is a property of a substance that represents the amount of heat required to raise the temperature of a unit mass (in grams) of that substance by one degree Celsius or Kelvin. To calculate the specific heat of lead, we can use the formula:
Q = m * c * ΔT
where Q is the heat transferred, m is the mass, c is the specific heat, and ΔT is the change in temperature.
In this case, we have:
Q = 54.0 J, m = 58.3 g, ΔT = 42.0°C - 12.0°C = 30.0°C.
Substituting these values into the formula, we get:
54.0 J = 58.3 g * c * 30.0°C
To calculate the specific heat, c, we divide both sides of the equation by (58.3 g * 30.0°C):
c = 54.0 J / (58.3 g * 30.0°C) = 0.031 J/(g°C)
Therefore, the specific heat of lead is 0.031 J/(g°C).