Problem 16.44 A cylinder contains oxygen gas (O2) at a pressure of 2.40atm . The

Question

Problem 16.44

A cylinder contains oxygen gas (O2) at a pressure of 2.40atm . The volume is 6.00L , and the temperature is 300K . Assume that the oxygen may be treated as an ideal gas. The oxygen is carried through the following processes:
(1) Heated at constant pressure from the initial state (state 1) to state 2, which has 440K.
(2) Cooled at constant volume to 250K (state 3).
(3) Compressed at constant temperature to a volume of 6.00L (state 4).
(4) Heated at constant volume to 300K , which takes the system back to state 1.

Part A

Calculate Q for each of the four processes.

Q1?2,Q2?3,Q3?4,Q4?1=

Part B

Calculate W for each of the four processes

W1?2,W2?3,W3?4,W4?1=

Part C

Calculate the net work done by the oxygen

Part D

What is the efficiency of this device as a heat engine?

Part E

How does the efficiency in part (D) compare with that of a Carnot-cycle engine operating between the same minimum and maximum temperatures of 250K and 440K. ?

Explanation / Answer

The numebr of moles is: n = PV/RT = 0.585 mol

Part A:

Q1 = 2382.1 J

Q2 = -2309.1 J

Q3=-464.7 J

Q4 = 607.7 J

Part B:

W1 = 680.6 J

W2 = 0

W3 = -464.7 J

W4 = 0 J

Part C:

The net work is: W = 215.9 J

Part D:

The efficiency is:
e =W/Qh = 215.9/2987.8 = 0.07226

Part E: we have for carnot :

e = 1-Tc/Th = 0.4318

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