Thermodynamics | Thermodynamic Processes#
A Thermodynamic process is a process in which the thermodynamic state of a system is changed.
1. Isochoric Process#
- In an isochoric process, volume remains constant.
\[V = constant\]
\[Change\ in\ volume\ (ΔV) = 0\]
2. Isobaric Process#
- Pressure is constant throughout an isobaric process.
\[P = constant\]
\[Change\ in\ Pressure\ (ΔP) = 0\]
3. Isothermal Process#
- In an isothermal process, temperature remains constant.
\[T = constant\]
\[Change\ in\ temperature\ (ΔT) = 0\]
\[Also,\ PV = nRT\]
\[Since,\ T = constant\]
\[P\ ∝\ {1 \over V}\]
\[Or,\ PV = constant\]
4. Adiabatic Process#
-
In an adiabatic process, there is no exchange of heat between system and surrounding.
-
The equation of an adiabatic process is given by:
\[PV^γ = constant\]
\[where,\ γ = Poisson's\ ratio\]
- We will discuss Poisson's ratio later. Note that γ is always greater than or equal to 1.
5. Cyclic Process#
-
A cyclic process is one in which a system returns to the initial state after going through different steps.
-
For a cyclic process, change in the value of a state function is always zero because state functions depend on initial and final state of the system and not on the path followed by the system.
How to distinguish between isothermal curve and adiabatic curve?#
Key Concept: Adiabatic curves are steeper as compared to isothermal curves at same temperature.
Example 1:#
- Here, red curve is steeper so it is adiabatic and green curve is isothermal.
Proof:#
\[Here,\ slope\ of\ graph = {dP \over dV}\]
\[For\ isothermal\ process:\]
\[PV = constant\]
\[PdV + VdP = 0\]
\[ {dP \over dV} = {-P \over V}\]
\[For\ adiabatic\ process:\]
\[PV^γ = constant\]
\[PγV^{γ-1}dV + V^γdP = 0\]
\[ {dP \over dV} = {-Pγ \over V} \]
- Seeing the slopes of both isothermal and adiabatic curves as calculated above, we can safely infer that adiabatic curves are steeper because γ is always greater than or equal to 1.
Example 2:#
- Here, green curve is steeper, so it is adiabatic and the red curve is isothermal.