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Thermodynamic process; isothermal expansion diagrams

Short answer

A thermodynamic process is the path of successive equilibrium states. For isothermal expansion: P-v diagram is a hyperbola (Pv=constant), T-v is horizontal, P-T is vertical.

Define thermodynamic process. Sketch P-v, T-v and P-T diagram for an ideal gas undergoing isothermal expansion.

A thermodynamic process is the path of successive equilibrium states followed by a system as it changes from an initial to a final state, e.g. isobaric, isochoric, isothermal, adiabatic.

Isothermal expansion of an ideal gas

T = constant, so PV = mRT = constant: P = C/V (rectangular hyperbola). On expansion, v increases and P decreases.

 P-v diagram        T-v diagram        P-T diagram
 P|                 T|                 P|  1
  |1                 |                  |  |
  | \                |1 ------> 2       |  |
  |  \_              |                  |  |
  |    \__ 2         |                  |  2
  +--------- v       +--------- v       +--------- T
 hyperbola Pv=C      horizontal line    vertical line
  • P-v: falling hyperbola from 1 to 2, with v₂ > v₁ and P₂ < P₁; area under the curve = W = mRT ln(V₂/V₁).
  • T-v: horizontal line at constant T.
  • P-T: a vertical line (T constant, P falls from P₁ to P₂).

✓ Answer checked by Claude Opus 5.5 (high effort)

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