Problem: An ideal monatomic gas is contained in a cylinder with a movable piston so that the gas can do work on the outside world, and heat can be added or removed as necessary. The figure shows various paths that the gas might take in expanding from an initial state whose pressure, volume, and temperature are , , and  respectively. The gas expands to a state with final volume . For some answers it will be convenient to generalize your results by using the variable , which is the ratio of final to initial volumes (equal to 4 for the expansions shown in the figure.)The figure shows several possible paths of the system in the pV plane. Although there are an infinite number of paths possible, several of those shown are special because one of their state variables remains constant during the expansion. These have the following names:Adiabiatic: No heat is added or removed during the expansion.Isobaric: The pressure remains constant during the expansion.Isothermal: The temperature remains constant during the expansion.Part ECalculate WA, the work done by the gas as it expands along path A from V0 to VA = RvV0.Express WA in terms of P0, V0, and Rv.W=

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Part E

For an isobaric process, the work done is expressed ad:

W = p(V2 - V1)

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Problem Details

An ideal monatomic gas is contained in a cylinder with a movable piston so that the gas can do work on the outside world, and heat can be added or removed as necessary. The figure shows various paths that the gas might take in expanding from an initial state whose pressure, volume, and temperature are p_0, V_0, and T_0 respectively. The gas expands to a state with final volume 4V_0. For some answers it will be convenient to generalize your results by using the variable R_v = V_{\rm final}/V_{\rm initial}, which is the ratio of final to initial volumes (equal to 4 for the expansions shown in the figure.)

The figure shows several possible paths of the system in the pV plane. Although there are an infinite number of paths possible, several of those shown are special because one of their state variables remains constant during the expansion. These have the following names:

  • Adiabiatic: No heat is added or removed during the expansion.
  • Isobaric: The pressure remains constant during the expansion.
  • Isothermal: The temperature remains constant during the expansion.

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Part E

Calculate WA, the work done by the gas as it expands along path A from V0 to VA = RvV0.

Express WA in terms of P0, V0, and Rv.

W=