Pressure-Volume Work and Path Dependence
For quasistatic compression or expansion with work by the system positive, W_by = ∫P dV; geometrically it is signed area under the P-V path, while ΔU depends only on endpoint states.
Why this shows up in the exam
Straight-line paths in P-V space · Comparing heat on alternate routes · Interpreting compression and expansion signs
Learn the idea
Quasistatic pressure-volume work is the signed area under the path on a P-V diagram. The same endpoints can be connected by paths with different areas, so work and heat can differ even though internal-energy change does not.
🧠 Memory hook: Area under the route is work; endpoints alone cannot fix it.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- W_by = ∫ P dV — signed boundary work for a quasistatic path; expansion is positive
- straight segment: W_by = (P_i+P_f)(V_f-V_i)/2 — trapezoid area when pressure varies linearly with volume
How to approach it
- 1Read axes and SI units
- 2Split the path into simple segments or integrate
- 3Assign the sign from the direction of volume change
Common slip-ups that cost marks
- •Using rectangle area for a sloping path
- •Forgetting volume-unit conversion
- •Assuming work is a state function
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A gas absorbs 500 J of heat and does 200 J of work. What is the change in its internal energy?
More from Thermodynamics
Thermodynamic Processes and P-V Diagrams
Study different thermodynamic processes (isothermal, isobaric, isochoric, adiabatic, polytropic, cyclic), their definitions, characteristics, and graphical representation on P-V diagrams.
Laws of Thermodynamics
Understand the zeroth and first laws of thermodynamics, including their statements, implications, and applications to physical systems.
Internal Energy, Heat, and Work
Explore the concepts of internal energy, heat, and work, including their definitions, relationships, and how they change during various thermodynamic processes.
Ideal Gas Law and Equation
Learn the ideal gas equation, its relation to physical quantities like pressure, volume, temperature, and density, and its use in describing the behavior of ideal gases.
Gibbs Free Energy and Spontaneity
Learn how Gibbs free energy determines spontaneity, how to calculate it, and its dependence on temperature, pressure, and other thermodynamic parameters.
Entropy and Its Changes
Understand entropy as a measure of disorder, how it changes in physical and chemical processes, and its calculation in various scenarios including phase transitions and isothermal processes.