PLEASE ANSWER ALL THE PARTS IN DETAILS

A well-insulated container consists of two halves of equal volumes V separated by a partition. On one half, there are N moles of a monatomic ideal gas at initial temperature Ti . On the other, there is a vacuum. The partition is suddenly removed, and the gas expands. Recall for a monatomic ideal gas that PV =NkBT and E =(3/2)NkBT. (a) Calculate the following quantities: the work done by the gas, the heat transferred to the gas, the change in energy, the change in entropy, the final temperature, and the final pressure. (b) Consider the relationship discussed in this chapter, Q = T dS. Why does an increase in entropy not correspond to a heat transfer in this case? (c) Instead of being suddenly removed, the partition is gradually moved to the empty side of the container so that the gas expands reversibly against the force of the partition. Repeat part (a) for this scenario