Calculating Heat Transfer Between Two Substances

Calculating heat transfer between two substances that start at different temperatures means setting the heat lost by the hotter substance equal in magnitude to the heat gained by the cooler one, since ideally no heat escapes to the outside environment.

A 360.0-g steel rod is dropped into 425 mL of water sitting at 24.0 °C, and the final temperature of both settles at 42.7 °C. Setting the rod's heat loss equal in magnitude to the water's heat gain, and substituting each substance's own mass and specific heat into that equation, leaves only the rod's unknown starting temperature to solve for. Working through the algebra gives an initial rod temperature near 248 °C, well above the boiling point of water, which is consistent with rebar fresh from a forge.