Answer:
To solve this problem, we can use the equation:
Q = m * c * ΔT
where Q is the heat transferred, m is the mass of the substance, c is its specific heat capacity, and ΔT is the change in temperature.
In this case, we know that the heat lost by the metal is equal to the heat gained by the water:
Q lost = Q gained
We can calculate the heat lost by the metal using the equation:
Q lost = m * c * ΔT
where m is the mass of the metal, c is the specific heat capacity of the metal (which we are trying to find), and ΔT is the change in temperature of the metal (100.5 C - 30.2 C = 70.3 C).
We can calculate the heat gained by the water using the equation:
Q gained = m * c * ΔT
where m is the mass of the water and ΔT is the change in temperature of the water (30.2 C - 20.0 C = 10.2 C).
Setting the two equations equal to each other, we get:
m * c * ΔT (metal) = m * c * ΔT (water)
Simplifying, we get:
c (metal) = (m * c * ΔT (water)) / (m * ΔT (metal))
Plugging in the values we know:
m (metal) = 32.8 g
ΔT (metal) = 70.3 C
m (water) = 138.2 g
ΔT (water) = 10.2 C
c (metal) = (138.2 g * 4.184 J/g·K * 10.2 C) / (32.8 g * 70.3 C)
c (metal) = 0.192 J/g·K
Therefore, the specific heat capacity of the metal is 0.192 J/g·K.