C

Step 1: We know that the total energy of the two systems is conserved, which can be expressed mathematically as:
$$ C_1 (T_1 - T_f) + C_2 (T_2 - T_f) = 0 $$
Step 2: Here, \(T_2\) is the initial temperature of system 2. Rearranging the equation gives us:
$$ C_1 (T_1 - T_f) = -C_2 (T_2 - T_f) $$
Step 3: Divide both sides by \(-C_2\) to isolate \(T_2\):
$$ T_2 - T_f = -\frac{C_1}{C_2} (T_1 - T_f) $$
Step 4: Finally, rearranging gives us the expression for \(T_2\):
$$ T_2 = T_f - \frac{C_1}{C_2} (T_1 - T_f) $$
Thus, the initial temperature of system 2 can be expressed in terms of the other variables.