A gas expands from I to F in the figure below. The energy added to the gas by heat is 212 J when the gas goes from I to F along the diagonal path. Three paths are plotted on a PV diagram, which has a horizontal axis labeled V (liters), and a vertical axis labeled P (atm). The green path starts at point I (2,4), extends vertically down to point B (2,1), then extends horizontally to point F (4,1). The blue path starts at point I (2,4), and extends down and to the right to end at point F (4,1). The orange path starts at point I (2,4), extends horizontally to the right to point A (4,4), then extends vertically down to end at point F (4,1). (a) What is the change in internal energy of the gas? Use the relations between various features of the graph and the work done on the gas to find the energy added by work and then use your result to find the change in internal energy of the gas. J (b) How much energy must be added to the gas by heat for the indirect path IAF to give the same change in internal energy? Calculate the work done on the gas from the appropriate area on the graph and apply the first law of thermodynamics with the known change in internal energy and the energy transferred by heat. J

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter21: Heat And The First Law Of Thermodynamics

Section: Chapter Questions

Problem 44PQ

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A gas expands from I to F in the figure below. The energy added to the gas by heat is 212 J when the gas goes from I to F along the diagonal path.

Three paths are plotted on a PV diagram, which has a horizontal axis labeled V (liters), and a vertical axis labeled P (atm).

The green path starts at point I (2,4), extends vertically down to point B (2,1), then extends horizontally to point F (4,1).
The blue path starts at point I (2,4), and extends down and to the right to end at point F (4,1).
The orange path starts at point I (2,4), extends horizontally to the right to point A (4,4), then extends vertically down to end at point F (4,1).

(a) What is the change in internal energy of the gas?

Use the relations between various features of the graph and the work done on the gas to find the energy added by work and then use your result to find the change in internal energy of the gas. J

(b) How much energy must be added to the gas by heat for the indirect path IAF to give the same change in internal energy?

Calculate the work done on the gas from the appropriate area on the graph and apply the first law of thermodynamics with the known change in internal energy and the energy transferred by heat. J

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