Cyclic and Isochoric Processes
Understanding systems at constant volume and systems that return to their initial state.
In thermodynamics, processes are defined by how state variables change. Here we explore two distinct types: the Isochoric Process (constant volume) and the Cyclic Process (where the system returns to its starting point).
1. Isochoric Process (Constant Volume)
An Isochoric (or Isometric) process is one where the volume of the system remains constant throughout ($\Delta V = 0$). This typically occurs in rigid, closed containers.
A. Key Relations (Gay-Lussac's Law)
From the ideal gas equation $PV = nRT$, if Volume ($V$) is constant: $$ P \propto T $$
Graph: The PV diagram is a vertical straight line parallel to the Pressure axis.
B. Work Done & Heat
Work Done
Since $dV = 0$, no expansion or compression work is done.
First Law Application ($\Delta U = q + w$):
Heat supplied at constant volume ($q_v$) is entirely used to increase Internal Energy.
2. Cyclic Process
A Cyclic Process is a series of thermodynamic operations where the system returns to its initial state.
A. State Functions Change
Since Internal Energy ($U$) and Enthalpy ($H$) are state functions (depend only on initial and final states), the net change over a full cycle is zero.
B. First Law for a Cycle
$$ \Delta U_{net} = q_{net} + w_{net} = 0 $$
Net heat exchanged equals the net work done (in magnitude).
C. Work Done from Graph
The net work done is equal to the area enclosed by the loop on the PV diagram.
- Clockwise Cycle: Net expansion usually exceeds compression. Work is done BY the system (Negative in Chemistry convention).
- Counter-Clockwise Cycle: Net compression exceeds expansion. Work is done ON the system (Positive in Chemistry convention).
Knowledge Check
Test your understanding of Cyclic & Isochoric Processes
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