Question 4 of 4 · The First Law in Closed-System Processes · Advanced · About 25 min

Two-stage heating and cooling sequence

A closed $1.30\,\mathrm{kg}$ ideal-gas charge at $310\,\mathrm{K}$ and $150\,\mathrm{kPa}$ first receives heat at constant pressure until $430\,\mathrm{K}$ . It then cools at constant volume to . Use , and . Determine the total boundary work, heat exchanged during each stage, net heat, and final pressure.

A two-stage ideal-gas path expands at fixed pressure then cools at fixed volume. — Schematic, not to scale unless dimensions are given.

Given

Mass 1.30 kg
Initial T1 310 K and P1 150 kPa
Intermediate T2 430 K
Final T3 365 K
R 0.287, cv 0.718, cp 1.005 kJ/(kg K)

Find

Total boundary work
Heat in first stage
Heat in second stage
Net heat
Final pressure

Assumptions

Ideal gas; reversible-equilibrium stages with no other work.

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Two-stage heating and cooling sequence

Given

Find

Assumptions

Worked solution