The Bermuda Triangle (see attachment)
A cylinder with initial volume V contains a sample of gas at pressure p. The gas is heated in such a way that its pressure is directly proportional to its volume. After the gas reaches the volume 3V and pressure 3p, it is cooled isobarically to its original volume V. The gas is then cooled isochorically until it returns to the original volume and pressure.
Find the work W done on the gas during the entire process.
MODEL: Assume that the gas is ideal and the process is quasi-static.
VISUALIZE: Show the process on a pV diagram. Note whether it happens to be one of the basic gas processes: isochoric, isobaric, or isothermal.
SOLVE: Calculate the work as the area under the pV curve either geometrically or by carrying out the integration: (see attachment)
ASSESS: Check your signs:
W > 0 when the gas is compressed. Energy is transferred from the environment to the gas.
W < 0 when the gas expands. Energy is transferred from the gas to the environment.
No work is done if the volume doesn't change: W = 0.
Questions:
1. It is reasonable to use the ideal-gas model in this problem if which of the following conditions are met?
a) The temperature is well below the condensation point.
b) The temperature is well above the condensation point.
c) The density of the gas is low.
d) The density of the gas is high.
e) The pressure of the gas is much greater than atmospheric pressure.
f) The pressure of the gas is much smaller than atmospheric pressure.
Enter the letters of all the correct answers alphabetically. Do not use commas. For instance, if you think the first three conditions are necessary, enter ABC.
2. The processes involved can be assumed to be quasi-static if which of the following holds? Please choose only one answer.
a) They happen slowly.
b) They occur at low enough pressure.
c) They occur at low enough volume.
d) They occur at high enough temperature.