Ideal-Gas Thermal Coefficients and Heat Capacities
For a gas the volume-expansion coefficient is beta = (1/V)(partial V/partial T) under the stated constraint, while ideal-gas molar heat capacities satisfy C_p-C_v=R and depend on allowed molecular degrees of freedom.
Why this shows up in the exam
Gas thermometers · Constrained ideal-gas expansion · Comparing constant-pressure and constant-volume heating
Learn the idea
Ideal-gas expansion and heat capacity depend on the specified constraint, not temperature alone. A gas can warm while pressure, volume, or another combination changes; differentiate the actual path equation before naming an expansion coefficient or required heat.
🧠 Memory hook: For gases, name the path before choosing the coefficient.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- beta_P = (1/V)(partial V/partial T)_P = 1/T — ideal-gas volume coefficient at constant pressure
- C_p - C_v = R — Mayer relation per mole for an ideal gas
- Q = n C_process Delta T — heat for a stated constant-pressure or constant-volume ideal-gas process
How to approach it
- 1Write the gas law and path constraint
- 2Express V as a function of absolute T
- 3Differentiate or select the matching process heat capacity
Common slip-ups that cost marks
- •Using beta=1/T for a nonconstant-pressure path
- •Confusing C_p with C_v
- •Using Celsius instead of absolute temperature in gas coefficients
🌟 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 wire 1 m long and cross-sectional area 2 mm^2 extends by 1 mm under a 200 N load. Find Young modulus.
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