Consider a very simple model of a computer memory, in which molecules are either found to reside in the left half of their memory cell (encoding a "0"), or in the right half (encoding a "1"). Imagine that we have a 10-bit register. Initially each cell is in the "0" state (i.e., all particles are in the left side of their respective cells); after the computation, they are in either half of the cell (depending on the specific computation). This doesn't necessarily require any work, e.g., if one simply pulls out (transverse to the axis of the memory) the dividing wall between the "0" and "1" side, the particles can by free expansion move from the "0" state into the "1" state.
Your task is to determine the energy cost to reset the 10-bit register to its initial state, where every particle is again in the "0" side of its cell. This can be done by using a piston to push the particles (~compressing the gas) so that they can only occupy the left side of the cell.
1. What is the change in (dimensionless) entropy in this process?
2. What energy is required to carry out the process?
The Attempt at a Solution
For the first question, i figured that N=10 and final Volume should be half of Initial Volume) because it says it has to occupy only the left side of the cell which is half
and hence the change in entropy would be 10*ln(1/2)..
Am i doing correctly?
For the 2nd question,I am totally stuck with this question.
I am guessing that the energy required would be neglect-ably small...?
Could someone help me out with these two questions ?