Module B.4 IBDP HL only Track

Thermodynamics

Deep dive into the first and second laws, cyclic processes, gas heat engines, and entropy shifts.

01. Observe 02. Think 03. Apply 04. Achieve Excellence

Thermodynamics

Introduction

Thermodynamics studies energy transfer at the level of whole systems. In the IB HL guide, this topic extends the gas model into the first law, entropy, engine cycles, and the unavoidable limits placed on useful work.

Guide Focus

  • Apply the first law Q = delta U + W using the IB sign convention.
  • Interpret entropy changes in isolated and non-isolated systems.
  • Analyse thermodynamic processes, heat engines, and Carnot efficiency.

Key Concepts

1. First law of thermodynamics

For a closed system, Q = delta U + W. Q is thermal energy supplied to the system, and W is work done by the system. For a gas changing volume at constant pressure, W = P delta V.

2. Internal energy of a monatomic ideal gas

The internal energy change is delta U = (3/2)NkB delta T = (3/2)nR delta T. Temperature change, not the path taken, determines delta U for an ideal monatomic gas.

3. Entropy

Entropy measures the number of possible microscopic arrangements consistent with a macroscopic state. It can be written as delta S = delta Q / T for reversible thermal transfer and S = kB ln Omega for microstates.

4. Processes and heat engines

Isovolumetric, isobaric, isothermal, and adiabatic processes keep one variable fixed. For a monatomic ideal gas in an adiabatic process, PV^(5/3) = constant. Cyclic processes can operate heat engines, with efficiency eta = useful work / input energy.

5. Carnot limit

No real engine can exceed the Carnot efficiency between two reservoirs: eta_Carnot = 1 - Tc / Th, where temperatures are in kelvin.

Common Mistakes

  • Mixing sign conventions for work done by and work done on the system.
  • Using Celsius in entropy or Carnot efficiency calculations.
  • Assuming a local entropy decrease violates the second law without considering surroundings.

Exam Tips

  • Start every first-law problem by defining the system.
  • On a PV diagram, area under the curve represents work done by the gas.
  • For a full cycle, delta U = 0 because the system returns to its original state.

Practice Questions

Question 1 (Multiple Choice)

A heat engine operates between reservoirs at 600 K and 300 K. What is the maximum possible efficiency?

A. 0.50 B. 0.25 C. 2.0 D. 0.75

Correct Answer: A

Solution Architecture

The Carnot limit is 1 - Tc / Th = 1 - 300 / 600 = 0.50.

Question 2 (Structured Paper 2 Style)

A gas receives 500 J of thermal energy and does 180 J of work on its surroundings.

(a) Calculate the change in internal energy. [2 marks]

(b) State whether the gas temperature increases for an ideal gas. [1 mark]

Paper 2 Structured Problem

Markscheme Breakdown

Part (a) Solution:

Using Q = delta U + W, delta U = Q - W = 500 - 180 = 320 J.

Part (b) Solution:

For an ideal gas, positive delta U means the temperature increases.