Halliday, Resnick & Walker — Temperature, Heat, and the First Law of Thermodynamics: Problem 74

In a series of experiments, block B is to be placed in a thermally insulated container with block A, which has the same mass as block B. In each experiment, block B is initially at a certain temperature \(T_B\), but temperature \(T_A\) of block A is changed from experiment to experiment. Let \(T_f\) represent the final temperature of the two blocks when they reach thermal equilibrium in any of the experiments. Figure 18.30 gives temperature \(T_f\) versus the initial temperature \(T_A\) for a range of possible values of \(T_A\), from \(T_{A1} = 0\text{ K}\) to \(T_{A2} = 500\text{ K}\). The vertical axis scale is set by \(T_{fs} = 400\text{ K}\). What are (a) temperature \(T_B\) and (b) the ratio \(c_B/c_A\) of the specific heats of the blocks?