Question

2. [4] Consider a box of volume V2 with a partition that separates a third of the box, Vi-V2 /3, from the rest. Initially, Vi contains N molecules of monatomic ideal gas at temperature tı, while the rest of the box is empty. The walls of the box are well insulated. (a) [1] The partition is suddenly removed. No heat enters or leaves the box during the sudden expansion of the gas. What is the final temperature of the gas, T2, after the sudden expansion! (b) [1] What is the change in entropy of the gas, Δσ, as a result of the sudden expansion? (c) [] How much work would you have to do to compress the gas back to its initial volume? Again, assume that no heat is transferred to the outside world. Express your answer in terms of N and t2. (This integral is a bit tricky. To avoid it, do part (d) first, then see if you can figure out an easier way to calculate the work done.) d) [1] What is the final temperature ' of the gas after the compression in part (c)? Express your answer in terms of τ2.

Answer 1

a) The walls of the box are insulated. Since there is no heat flow we do not expect any change in internal energy in free expansion. That is there will be no change in temperature of the ideal gas.
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