Suppose 550 g of water at 32 degrees * C is poured into a 210 - g aluminum can with an initial temperature of 15 degrees * C . Find the final temperature of the system, assuming that no thermal energy is exchanged with the surroundings.

about 30.714degC

Explanation:

Assuming

specific heat of water at  4200 J/kg * K

specific heat of aluminum 900 J/kg * K

(actual values to higher precision differ, and also change slightly with temperature).

To raise the aluminum's temp by 1K we need 900J * (210g / 1kg) = 189J

189J given by the water decreases its temp by 1K * (189J / 4200J) * (1kg / 550g) = 0.0(81)K.

So every K the temp of aluminum rises, 0.0(81)K falls the temp of the water.

At a difference of (32degC - 15degC) = 17K, we infer the temp will balance out after 17K / (1K + 0.0(81)K) "steps", so about 15.714.

The final temperature will be around 30.714degC