Isothermal Process
* Definition: An isothermal process occurs at constant temperature.
* Work Done: The work done in an isothermal process is given by:
```
W = nRT * ln(V₂/V₁)
```
where:
* W is the work done
* n is the number of moles of gas
* R is the ideal gas constant
* T is the constant temperature
* V₁ is the initial volume
* V₂ is the final volume
* Explanation: In an isothermal process, the internal energy of the system remains constant (since temperature is constant). Therefore, all heat added to the system is used to do work on the surroundings. The natural logarithm term reflects the expansion or compression of the gas.
Adiabatic Process
* Definition: An adiabatic process occurs with no heat exchange between the system and its surroundings (Q = 0).
* Work Done: The work done in an adiabatic process is given by:
```
W = (P₂V₂ - P₁V₁) / (1 - γ)
```
where:
* W is the work done
* P₁ and V₁ are the initial pressure and volume
* P₂ and V₂ are the final pressure and volume
* γ is the adiabatic index (ratio of specific heats, Cp/Cv)
* Explanation: In an adiabatic process, the system is isolated from its surroundings, so the work done is entirely at the expense of the internal energy of the system. The adiabatic index γ represents the relationship between heat capacity at constant pressure (Cp) and constant volume (Cv), which is specific to the gas.
Key Points to Remember
* Sign Convention: Work is positive when the system does work on the surroundings (expansion). Work is negative when work is done on the system (compression).
* Ideal Gas Assumptions: These formulas are based on the ideal gas law. In reality, real gases may deviate from these expressions.
* Applications: These expressions are fundamental in thermodynamics, especially in understanding how engines and other systems operate.
Let me know if you'd like more details or have any specific scenarios you'd like to explore!
