A 17.0 g sample of quartz, which has a specific heat capacity of 0.730 Jg , is dropped into an insulated container containing 200.0 g of water at 85.0 °C and a constant pressure of 1 atm. The initial temperature of the quartz is 7.2 ℃. Assuming no heat is absorbed from or by the container, or the surroundings, calculate the equilibrium temperature of the water. Be sure your answer has 3 significant digits. ec

Assuming that no heat is absorbed from the container , then all the heat absorbed by the water Q water comes from the heat released by the quartz (-Q quatz), since

Q water + Q quatz = Q surroundings =0

denoting w as water and q as quartz then

Q water = mw * cpw * (Tfinal - T initial w)

Q quartz = mq * cpq * (Tfinal - T initial q)

where

m= mass

cp= specific heat capacity at constant pressure

T final = final temperature

T initial w and T initial q = initial temperature of water and quartz respectively

then

mw * cpw * (Tfinal - T initial w) + mq * cpq * (Tfinal - T initial q) = 0

mw * cpw * Tfinal + mq * cpq * Tfinal = mw * cpw *T initial w + mq * cpq * T initial q

Tfinal = (mw * cpw *T initial w+ mq * cpq * T initial q)/(mw * cpw +mq * cpq)

replacing values and assuming cpw= 1 cal/gr°C = 4.186 J/g°C

Tfinal = (200 g * 4.186 J/g°C * 85 °C + 17g * 0.730 J/g°C * 7.2 °C)/(200 g * 4.186 J/g°C + 17g * 0.730 J/g°C) = 83.863 °C

Tfinal = 83.863 °C