Final answer:
The question lacks the necessary efficiency percentage to determine the total work the steam must do on the turbine based on the given useful work of 2.64 x 10^2 J. Typically, the total work input is derived by dividing the useful work output by the efficiency of the turbine.
Step-by-step explanation:
The question relates to the efficiency of a steam turbine which is considered the most efficient type of steam engine. To find the total work the steam must do on the turbine given the useful work output, we must consider the efficiency of the turbine.
Since the efficiency of an engine is calculated as the useful work output divided by the total work input (also representing the heat energy transferred into the engine), if we know that the turbine's useful work done each second is 2.64 x 10^2 J, we can set up a simple equation to find the total work input required to produce this output if the efficiency is given.
The problem seems to be missing the key piece of information regarding the actual efficiency percentage, which is necessary to calculate the exact amount of total work input needed. Without this percentage, many of the figures provided in the question cannot be specifically answered. Assuming a hypothetical efficiency, for example, a 50% efficient turbine would require twice the work output (2 x 2.64 x 10^2 J = 5.28 x 10^2 J) as total work input, which would ideally be our answer. However, the exact answer will change depending on the given efficiency of the steam turbine.