Consider the four-process cycle shown in the P-V diagram in the figure above. Th
ID: 1988296 • Letter: C
Question
Consider the four-process cycle shown in the P-V diagram in the figure above. The graph shows a sequence of four processes being carried out on a sealed system of ideal gas. In this case, P is 30.0 kPa and V is 3.00 liters.
(a) Calculate the work done by the gas in the process taking the system from state 1 to state 2. (J)
(b) Calculate the work done by the gas in the process taking the system from state 2 to state 3. (J)
(c) Calculate the work done by the gas in the process taking the system from state 3 to state 4. (J)
(d) Calculate the work done by the gas in the process taking the system from state 4 to state 1. (J)
(e) Calculate the net work done by the gas in one entire cycle. (J)
(f) Calculate the net change in the internal energy of the gas for one entire cycle. (J)
(g) Calculate the net heat added to the gas for one entire cycle. (J)
(h) Complete this sentence - The temperature in state 3 is larger than the temperature in state 1 by a factor of ___?___.
For the last two parts, assume that the ideal gas in this system is monatomic.
(i) Calculate the change in internal energy experienced by the gas during the process that takes the system from state 1 to state 2. (J)
(j) Calculate the heat added to the gas for the process that takes the system from state 1 to state 2. (J)
Explanation / Answer
First off, this is an extremely long question... you're welcome. In the future break this up into multiple parts. Work is area under the curve, so just count squares and multiply by the area of each individual square. a) 1.5*15*8 = 180 J b) 1.5*15*12 = 270 J c) 0 J - no work done because it is a straight line d) -1.5*15*12 = -270 J e) 180 + 270 + 0 + -270 = 180 J f) 0 J g) 180 J (same as e) h) use ratios. state 3 is at 3P and 3V whereas 1 is at 1P and 1V. 1*1 = 1 and 3*3 = 9. Compare 9 to 1. Factor of 9. i) 15 (P1) (v1) / 2 15 (30) (3) / 2 = 675 J j) part a + part i. 180 + 675 = 855 J