Thermodynamics Lecture Summary

Key Topics Covered

• Solving thermodynamic problems
• Processes: isothermal, isochoric, adiabatic, isobaric
• Important equations for work, heat, and internal energy

Important Equations

General Equations

• First Law of Thermodynamics: \Delta U = Q - W
  • (Q): Heat added to the system
  • (W): Work done by the system
  • (\Delta U): Change in internal energy

Process-Specific Equations

Isocoric (Constant Volume)

• (\Delta V = 0) (Work (W = 0))
• (\Delta U = Q = nC_V\Delta T)
• (Q = V \cdot C_V \cdot \Delta P / R)

Isobaric (Constant Pressure)

• (\Delta P = 0)
• (W = P \cdot \Delta V) or (W = nR \Delta T)
• (Q = nC_P \Delta T) or (Q = P \cdot C_P \cdot \Delta V / R)
• Use Charles's Law: (V_1/T_1 = V_2/T_2)

Isothermal (Constant Temperature)

• (\Delta T = 0)
• (\Delta U = 0), thus (Q = W)
• (W = nRT \ln(V_{\text{final}}/V_{\text{initial}}))
• (P_1V_1 = P_2V_2) (Boyle's Law)

Adiabatic (No Heat Exchange)

• (Q = 0)
• (\Delta U = -W)
• (\Delta U = nC_V\Delta T)
• (P_1V_1^\gamma = P_2V_2^\gamma)
• (T_1V_1^{\gamma-1} = T_2V_2^{\gamma-1})

Concepts

Thermodynamic Terms

• Work (W): Positive if done by the system; negative if done on the system.
• Heat (Q): Positive if absorbed; negative if released.
• Internal Energy (U): Related to temperature; changes with (\Delta U).

System Types

• Open System: Matter and energy can enter/leave.
• Closed System: Only energy can enter/leave.
• Isolated System: No matter or energy exchange.

Specific Heat Capacities

• Monoatomic Gases:
  • (C_V = \frac{3}{2}R)
  • (C_P = \frac{5}{2}R)
• Diatomic Gases:
  • (C_V = \frac{5}{2}R)
  • (C_P = \frac{7}{2}R)
• Polyatomic Gases: (Approximate for three atoms)
  • (C_V \approx \frac{7}{2}R)
  • (C_P \approx \frac{9}{2}R)

Cyclic Processes

• Net heat flow (Q = W) for cyclic processes
• Work done is equal to the area enclosed in a PV diagram.

Practice Problems

• Calculate internal energy change given heat and work.
• Isothermal and adiabatic processes: Derive final temperature and pressure.
• Application of thermodynamic laws in real-world scenarios like car engines.

Efficiency and Performance

• Efficiency of Engines: Calculated as (\eta = \frac{W}{Q_H} \times 100%)
• Heat Transfer: Understanding how heat is absorbed or released by systems during various processes.

This summary provides a comprehensive overview of thermodynamic processes and calculations essential for understanding heat, work, and energy changes in various systems.