One mole of gas in a closed system undergoes a four-step thermodynamic cycle. Use the data given in the following table to determine numerical values for the missing quantities indicated by question marks.

Question

What will be an ideal response?

Answer 1

For this problem, we need to use two principles: = Q + W , which gives us the 3rd number in any row in which we already have 2 numbers, and is a state function, so its value doesn’t change in a cyclic process (if we end up at the same conditions as where we started, will return to its initial value).



So, we just go through and fill in the numbers by adding and subtracting things. Q for the first step has to be Q = ?W = 5800 J. Likewise, =Q + W = ?500 or the third step. Also, for the whole cycle is 0, as stated

above. Filling these in gives



Now, we can fill in Q = 1400 J for the overall cycle (so Q + W = ). Then we know all but one number in the columns for and Q, and the sum of the 4 steps in each case has to add up to the value for the overall cycle, so we have = 0 + 200 + 500 ? 4700 = ?4000 J and = 1400?5800+3800+800 = 200. Filling these in gives:



Finally, we now know two of the three entries in the 2nd and 4th rows, so we can fill in these last two numbers. In each case, we have W = ? Q, which gives W = ?200 J for step 23 and W = 4500 J for step 41. Filling these in completes the table:



As a check, we can add up the work values for the four steps and make sure the sum comes out to be ?1400 (it does).