© Copyright, Department of Physics, University of Illinois at Urbana-Champaign

Heat Capacity of Solids

A 200-gram block of aluminum (Al, 27 g/mole) with an initial temperature TAl = 76.85 °C is brought into contact with a 500-gram block of copper (Cu, 63.5 g/mole) with an initial temperature TCu = 26.85 °C. Together the two blocks reach a final equilibrium temperature TF.

Assume that the blocks only exchange heat with one another, and that the blocks do not change in volume.

Let TF be the final temperature calculated using the Einstein model of solids where each metal block can be treated as a three dimensional lattice of balls on springs. The drawing shows two dimensions of the 3-dimensional lattice. Atoms (red balls) oscillate around their nominal positions (blue dots). Springs represent the potential V = (k/2) (x2 + y2 + z2). In this approximation, we find the heat capacity at constant volume using the equipartition theorem.

What is the final temperature of the two blocks in this approximation?

TF = °C