The specific heat (c) of a substance is the amount of heat energy required to raise the temperature of 1 gram of the substance by 1 degree Celsius. The formula for calculating the specific heat is:
q = mcΔT
where q is the heat energy absorbed by the substance, m is the mass of the substance, c is the specific heat, and ΔT is the change in temperature.
In this problem, we are given:
Mass of the metal (m) = 342.0 g
Initial temperature (T1) = 21.3°C
Final temperature (T2) = 46.3°C
Heat absorbed by the metal (q) = 291.7 J
First, we need to calculate the change in temperature (ΔT):
ΔT = T2 - T1 = 46.3°C - 21.3°C = 25°C
Next, we can use the formula for specific heat to solve for c:
q = mcΔT
c = q / (mΔT)
Substituting the given values, we get:
c = 291.7 J / (342.0 g x 25°C) = 0.034 J/g°C
Therefore, the specific heat of the unknown metal is 0.034 J/g°C.