Thermodynamics (Copy)

A2 Level Physics – Section 16: Thermodynamics (Detailed Notes)

16.1 Internal Energy

1. Definition of Internal Energy

• Internal energy (U): The total energy associated with the random motion and interactions of the molecules in a system.
• It is a state function: depends only on the state (e.g. temperature, pressure, volume), not on how the system got there.

Internal energy = Kinetic energy (EK) + Potential energy (EP)

• EK: due to random molecular motion (translation, rotation, vibration)
• EP: due to intermolecular forces (negligible in ideal gases)

2. Temperature and Internal Energy

• Temperature is directly related to the average kinetic energy of molecules.
• When temperature increases, internal energy increases, mainly due to a rise in molecular kinetic energy.
• For ideal gases:
  • Internal energy depends only on temperature
  • No intermolecular forces → EP ≈ 0

16.2 First Law of Thermodynamics

1. Work Done at Constant Pressure

• When a gas expands or is compressed at constant pressure, the work done (W) is:

W = p·ΔV

• W = work done (J)
• p = pressure (Pa)
• ΔV = change in volume (m³)

Important Sign Conventions:

• W > 0: work done by the gas (expands)
• W < 0: work done on the gas (compressed)

2. First Law of Thermodynamics

∆U = q + W

Where:

• ∆U = change in internal energy (J)
• q = heat added to the system (J)
• W = work done on the system (J)

Alternate signs used in some texts:

• ∆U = q – W (if W = work done by system)

Interpretation:

• Adding heat (q > 0) → increases internal energy
• Doing work on gas (W > 0) → increases internal energy
• Doing work by gas (W < 0) → decreases internal energy
• For ideal gases, internal energy depends only on temperature, so ∆U ∝ ∆T

Summary:

• Heating → increases kinetic energy of molecules
• Compression → increases potential interactions (in real gases) and kinetic energy
• Expansion without heat → decreases internal energy (gas cools)