Final answer:
The initial volume of mercury is 34 cm³.
Step-by-step explanation:
The volume of the unfilled part of the vessel remains constant at all temperatures when both the glass vessel and the mercury inside it are heated together. This means that the expansion of the mercury due to heating is compensated by the expansion of the glass vessel. Since the volume of the empty part of the vessel is given as 34 cm³, the initial volume of the mercury is also 34 cm³.