Thermodynamics Work & Processes

Work Done By Gases

• Work (W) done by a gas during expansion or compression is calculated as:
  • ( W = -\int P , dV )
• Positive work is done by the gas when it expands (increases volume).
• Negative work is done on the gas when it is compressed (decreases volume).

Adiabatic Processes

• An adiabatic process occurs without heat exchange with surroundings (Q = 0).
• Key characteristics:
  • For an ideal gas, the relationship between pressure, volume, and temperature can be expressed as:
    • ( PV^\gamma = \text{constant} )
    • ( T V^{\gamma - 1} = \text{constant} )
    • ( T P^{(1 - \gamma)/\gamma} = \text{constant} )
  • ( \gamma ) is the heat capacity ratio ( C_p/C_v ).
• Work done in adiabatic processes can be derived from changes in internal energy.

Isothermal Processes

• An isothermal process occurs at constant temperature (T).
• For an ideal gas, the relationship is given by:
  • ( PV = nRT ) (Ideal Gas Law)
• Work done during an isothermal expansion or compression is calculated as:
  • ( W = nRT \ln\left(\frac{V_f}{V_i}\right) )
• Heat exchange (Q) occurs to maintain constant temperature.

PV Diagrams

• PV diagrams graphically represent the relationship between pressure (P) and volume (V) for a thermodynamic process.
• Important aspects:
  • The area under the curve represents the work done.
  • Different curves indicate different processes (isothermal, adiabatic, etc.).
  • Steeper curves generally indicate higher pressures for a given volume.

First Law Of Thermodynamics

• Statement: Energy cannot be created or destroyed, only transformed.
• Mathematically expressed as:
  • ( \Delta U = Q - W )
  • Where ( \Delta U ) is the change in internal energy, Q is the heat added to the system, and W is the work done by the system.
• Applies to all thermodynamic processes, linking heat transfer and work.

Work Done By Gases

• Work done by a gas during expansion/compression is expressed as ( W = -\int P , dV ).
• Gas expands (volume increases) when it does positive work; compresses (volume decreases) when it experiences negative work.

Adiabatic Processes

• An adiabatic process involves no heat exchange with surroundings (Q = 0).
• For ideal gases, pressure, volume, and temperature relationships include:
  • ( PV^\gamma = \text{constant} )
  • ( T V^{\gamma - 1} = \text{constant} )
  • ( T P^{(1 - \gamma)/\gamma} = \text{constant} )
• The heat capacity ratio is denoted as ( \gamma = C_p/C_v ).
• Work in adiabatic processes can be determined through changes in internal energy.

Isothermal Processes

• An isothermal process occurs at a constant temperature (T).
• For an ideal gas, follows the Ideal Gas Law: ( PV = nRT ).
• Work performed during isothermal expansion/compression is given by:
  • ( W = nRT \ln\left(\frac{V_f}{V_i}\right) ).
• Heat exchange (Q) is necessary to keep the temperature constant throughout the process.

PV Diagrams

• PV diagrams visually depict the relationship between pressure (P) and volume (V) during thermodynamic processes.
• The area under a curve in the diagram represents the work done by or on the gas.
• Different curves represent distinct processes such as isothermal or adiabatic.
• Steeper curves indicate higher pressures for a corresponding volume.

First Law Of Thermodynamics

• The first law states that energy cannot be created or destroyed, but only transformed.
• It can be mathematically expressed as:
  • ( \Delta U = Q - W ), where ( \Delta U ) is the change in internal energy, Q is the heat added, and W is the work done by the system.
• This principle is applicable to all thermodynamic processes, establishing a fundamental relationship between heat transfer and work done.

This quiz explores the concepts of work done by gases, including adiabatic and isothermal processes. Understand the mathematical relationships and principles that govern the behavior of gases during expansion and compression. Test your knowledge on how energy is transferred and transformed within these thermodynamic processes.