Thermodynamic processes (isothermal adiabatic isobaric isochoric)

Processes as paths

A thermodynamic process is a change from one equilibrium state to another. On a pressure-volume diagram, the process is represented by a path. The path matters because heat and work depend on the process, not only on the endpoints.

For an ideal gas,

$PV=nRT$

and internal energy depends only on temperature. For a monatomic ideal gas,

U=rac{3}{2}nRT

so

Delta U=rac{3}{2}nRDelta T

Different processes produce different heat and work values for the same initial state.

Isothermal process

An isothermal process occurs at constant temperature:

$Delta T=0$

For an ideal gas, this means

$Delta U=0$

The first law becomes

$0=Q-W$

so

$Q=W$

For a reversible isothermal expansion of an ideal gas,

ight)$$ Heat must enter the gas during expansion to keep temperature constant while the gas does work. ## Adiabatic process An adiabatic process has no heat transfer: $$Q=0$$ The first law gives $$Delta U=-W$$ For an ideal gas expanding adiabatically, the gas does work, so internal energy and temperature decrease. For a reversible adiabatic process, $$PV^gamma=constant$$ where $$gamma=rac{C_P}{C_V}$$ Other useful forms are $$TV^{gamma-1}=constant$$ and $$T^gamma P^{1-gamma}=constant$$ ## Isobaric process An isobaric process occurs at constant pressure. Work is $$W=PDelta V$$ If a gas expands at constant pressure, it does positive work. Heat added goes partly into increasing internal energy and partly into expansion work. At constant pressure, heat transfer for an ideal gas is $$Q=nC_PDelta T$$ This is why $C_P$ includes the energy required for expansion work. ## Isochoric process An isochoric process occurs at constant volume: $$Delta V=0$$ Since $$W=int P,dV$$ the work is zero: $$W=0$$ The first law becomes $$Delta U=Q$$ For an ideal gas, $$Q=nC_VDelta T$$ All heat added at constant volume goes into changing internal energy. ## Comparing PV curves On a PV diagram, isobaric processes are horizontal lines, and isochoric processes are vertical lines. Isothermal curves for ideal gases satisfy $PV=constant$. Reversible adiabatic curves are steeper than isotherms during expansion because pressure drops faster when no heat enters. The area under any process curve gives work done by the gas. ## The big idea Isothermal, adiabatic, isobaric, and isochoric processes are idealized but essential thermodynamic paths. They differ by what is held constant or what transfer is forbidden. Understanding these processes builds the foundation for heat engines, refrigerators, atmospheric physics, and real thermodynamic cycles.