Isobaric Heating and First-Law Energy Split
With work by the gas positive, the first law is Q=Delta U+W; for a fixed ideal-gas sample heated isobarically, W=nRDelta T and Q=nC_PDelta T.
Why this shows up in the exam
Piston heating · Finding heat from stated work · Comparing temperature rises at constant P and V
Learn the idea
At constant pressure, supplied heat divides between internal-energy rise and boundary work. The expanding gas pushes a piston while warming, so the heat input is larger than the internal-energy increase by exactly the work done.
🧠 Memory hook: At constant pressure, heat pays for warming plus pushing.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- Q = Delta U + W — first law with W defined as work done by the gas
- W = P Delta V = nR Delta T — isobaric ideal-gas work at constant external pressure
- Delta U/Q = C_V/C_P = 1/gamma — fraction of isobaric heat stored internally for constant heat capacities
How to approach it
- 1State the work convention
- 2Use the process constraint to find W
- 3Apply Q=Delta U+W and check energy units
Common slip-ups that cost marks
- •Using Q=Delta U at constant pressure
- •Reversing the work sign convention
- •Using PDelta V when pressure varies
🌟 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 has rms molecular speed 300 m/s at 300 K. What is its rms speed at 1200 K, assuming ideal behavior?
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