Final answer:
To calculate the specific heat of the metal, use the formula q = mc∆T. Set up the equation mc(Metal)∆T(Metal) = mc(Water)∆T(Water). Solve for the specific heat of the metal using the given values.
Step-by-step explanation:
To calculate the specific heat of the metal, we can use the formula: q = mc∆T, where q is the heat gained or lost, m is the mass, c is the specific heat, and ∆T is the change in temperature. In this case, the heat gained by the metal is equal to the heat lost by the water. We can set up the equation: mc(Metal)∆T(Metal) = mc(Water)∆T(Water). Since the metal and water came to the same temperature, ∆T(Metal) = ∆T(Water). Solving for the specific heat of the metal, we get:
c(Metal) = (m(Water) x c(Water) x ∆T(Water)) / (m(Metal) x ∆T(Metal)).
Plugging in the given values:
c(Metal) = (105 g x 4.18 J/g°C x (33.80°C - 23.50°C)) / (175 g x (33.80°C - 93.50°C)).
Simplifying:
c(Metal) = 6.72 J/g°C.