Thermodynamic Bulk Modulus and Compressibility
The process bulk modulus is B = −V(dP/dV) along the stated path; an ideal gas has B_T = P isothermally and B_S = γP for a reversible adiabatic change.
Why this shows up in the exam
Isothermal gas compression · Speed-of-sound thermodynamic correction · Power-law pressure-volume relations
Learn the idea
Bulk modulus measures how strongly pressure must change to produce a fractional volume decrease along a specified process. The same gas resists compression differently when heat can escape than when it is thermally insulated.
🧠 Memory hook: Different paths give different gas stiffness.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- B = -V dP/dV — bulk-modulus definition along the specified thermodynamic path
- B_T = P — isothermal ideal-gas bulk modulus
- B_S = γP — reversible adiabatic ideal-gas bulk modulus
How to approach it
- 1Identify the path equation
- 2Differentiate pressure with respect to volume
- 3Check that the resulting modulus is positive for stable compression
Common slip-ups that cost marks
- •Omitting the minus sign in the definition
- •Using γP for a liquid without justification
- •Failing to state whether compression is isothermal or adiabatic
🌟 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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