A sample of gas is taken from state X ( ) to state Y ( ) by two different paths

PHYSICS · Single correct · AP · Physics 2: Algebra-based · Thermodynamics · Thermodynamics

Problem

A sample of gas is taken from state X (

100\,\text{kPa},\;0.020\,\text{m}^3

) to state Y (

200\,\text{kPa},\;0.040\,\text{m}^3

) by two different paths. • Path 1: The gas first expands isobarically to

0.040\,\text{m}^3

and then is compressed isochorically to

200\,\text{kPa}

. • Path 2: The gas first increases its pressure isochorically to

200\,\text{kPa}

and then expands isobarically to

0.040\,\text{m}^3

. Which of the following correctly compares the magnitude of the work done BY the gas along the two paths? (a) The work is greater along Path 1 because the area under its

P\!-\!V

curve is larger. (b) The work is the same for both paths because they share the same initial and final states. (c) The work is greater along Path 2 because the gas expands at the higher pressure of

200\;\text{kPa}

. (d) No work is done along either path because each path contains an isochoric segment.

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