A 35.2-g sample of an alloy at 93.0°C is placed into 219 g of water at 22.0°C in an insulated coffee cup. Assume that no heat is absorbed by the cup. If the final temperature of the system is 31.1°C, what is the specific heat capacity of the alloy in J / (g. K) ? Don't include units. cH2O = 4.184 J/g. K

mass of the alloy = 35.2 g

temperature t of the alloy = 93° C

heat loss by alloy = mc (t₁ - t₂) where t₁ = 93 and t₂ = 31.1° C

heat loss by alloy = 2178.88 c where c is the specific heat capacity of the alloy

heat gained by water = m cw (t₂ - t₁) where t₁ of water = 22° C and t₂ of water = 31.1° C

heat gained by water = 8338.294

heat gained = heat loss

2171.84 c = 8338.294

c specific heat capacity of the alloy = 8338.294 / 2178.88 = 3.83 J/g. K