Question 4 of 4 · Ideal Gases and Property Relations · Advanced · About 22 min

Combining two insulated gas chambers

Two rigid, insulated compartments contain the same ideal gas. Compartment A has $1.10\,\mathrm{kg}$ at $335\,\mathrm{K}$ in $0.260\,\mathrm{m^3}$ ; compartment B has $0.650\,\mathrm{kg}$ at $285\,\mathrm{K}$ in $0.190\,\mathrm{m^3}$ . A valve opens and the gas reaches one uniform state. Take $R=0.287$ and constant $c_v=0.718\,\mathrm{kJ/(kg\,K)}$ . Determine the final temperature and absolute pressure.

Two insulated ideal-gas chambers mix through an opened internal valve. — Schematic, not to scale unless dimensions are given.

Given

mA 1.10 kg, TA 335 K, VA 0.260 m³
mB 0.650 kg, TB 285 K, VB 0.190 m³
R 0.287 and cv 0.718 kJ/(kg K)

Find

Final temperature
Final pressure

Assumptions

Combined tank insulated and rigid; no external work; both contain the same ideal gas.

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Combining two insulated gas chambers

Given

Find

Assumptions

Worked solution