Reading and Transforming Thermodynamic Diagrams
For a fixed ideal gas, every plotted state satisfies PV = nRT; a process curve is transformed by combining this equation with its constraint, while orientation and endpoint ordering must remain physically consistent.
Why this shows up in the exam
Matching P-V and V-T cycles · Ordering isothermal and adiabatic curves · Identifying isobaric and isochoric legs
Learn the idea
Use the ideal-gas equation and process constraints to translate consistently among P-V, P-T, and V-T plots. A straight or curved line can look different after changing axes, so identify what remains constant before matching shapes.
🧠 Memory hook: Name the constraint before trusting the curve shape.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- P = nRT/V — conversion relation among P, V, and T for fixed ideal-gas amount
- isobaric: V/T = constant; isochoric: P/T = constant — straight proportionalities in V-T and P-T diagrams using kelvin temperature
- adiabatic: TV^(γ-1) = constant — constraint used to transform a reversible adiabatic leg
How to approach it
- 1Label each endpoint with P, V, and T relations
- 2Transform one leg at a time
- 3Check continuity, direction, and relative steepness
Common slip-ups that cost marks
- •Treating Celsius as a proportional temperature axis
- •Losing the direction of traversal
- •Calling every hyperbola isothermal without checking scale and constraint
🌟 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?
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