Thermodynamics - Work

Energy Exchange and Work

• Two ways of energy exchange:
  • Heat (when there is a temperature difference)
  • Work (when mechanical work is done)
• Work: The mechanical way to exchange energy

Formula for Work

• Formula: ( \text{Work} = -P_{\text{external}} \Delta V )
  • ( P_{\text{external}} ): External pressure
  • ( \Delta V ): Change in volume
• Expansion: ( \Delta V ) is positive, work is negative
• Compression: ( \Delta V ) is negative, work is positive

Derivation

• Derivation of work formula:
  • ( \text{Force (F)} = \text{Pressure (P)} \times \text{Area (A)} )
  • ( \text{Volume Change} \ (\Delta V) = \text{A} \times \Delta x )
  • ( \text{Work done} \ (W) = -\text{P}_{\text{external}} \Delta V )

When Pressure is Variable

• Use integration to find work:
  • ( W = -\int_{V_1}^{V_2} P , dV )

Using Graphs

• Area under PV curve in graph = Work done
• Calculate work using the area of trapezium or other shapes

Cyclic Processes

• Work in cyclic process: ( \text{Work} \neq 0 )
• ( \text{Work done in cycle} = \text{Area of cycle} )
• Clockwise = negative, Anticlockwise = positive

Questions

1. A gas expands up to 0.5 meters, calculate the work
2. Work done in cyclic process: using the graph

Important Notes

• Work is a path function, not a state function
• ( 1 \text{ atm liter} = 101.3 \text{ joules} )

Next Video

• Calculation of work in different thermodynamic processes
  • Isobaric, Isochoric, Isothermal, Adiabatic processes

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Note: Future videos will cover work in thermodynamic processes in detail.