Answer:
the final temperature is T final = 308 K
Explanation:
since all heat released by gold is absorbed by water
Q gold + Q water = Q surroundings =0 (insulated)
Assuming first that no evaporation of water occurs , and denoting g as gold and w as water , then
Q gold = m g*cp g* ( T final - T initial g)
Q gold = m w*cp w* ( T final - T initial w)
where
m= mass
cp = specific heat capacity
T final = final temperature
T initial g and T initial w = initial temperature of gold and water respectively
thus
Q gold + Q water = 0
m g*cp g* ( T final - T initial g) + m w*cp w* ( T final - T initial w) =0
m g*cp g* T final + m w*cp w* T final = m g*cp g* T initial g+ m w*cp w* T initial w
T final = (m g*cp g* T initial g+ m w*cp w* T initial w)/(m g*cp g+ m w*cp w)
replacing values and assuming cp w = 1 cal/gK = 4.816 J/gK and cp g = 0.129 J/gK (from tables), then
T final = (75 g*0.129 J/gK* 1000 K + 200 g * 4.816 J/gK * 300 K )/(75 g*0.129 J/gK*+ 200 g * 4.816 J/gK ) = 308 K
T final = 308 K
since T boiling water = 373 K and T final = 308 K , we confirm that water does not evaporate
therefore the final temperature is T final = 308 K
