A horizontal insulated cylinder has a frictionless non-conducting piston with 40 litres of air at 1 atm and 300 K on each side ( γ = 1.4 ). The left air is heated slowly until the right air is compres

Question

A horizontal insulated cylinder has a frictionless non-conducting piston with 40 litres of air at 1 atm and 300 K on each side ( γ = 1.4 ). The left air is heated slowly until the right air is compressed to 3 atm. Find the heat added to the left air, in kJ (one decimal, 1 atm = 1.013 × 1 0 5 Pa).

TestHub · Accepted Answer

n = RT P V ​ = 1.625 mol. Right (adiabatic): T r ​ = 300 × 3 0.2857 = 410.6 K, V r ​ = 40 × 3 − 1.4 1 ​ = 18.2 litre, so the work on it is n C v ​ Δ T = 3.74 kJ. Left: V = 80 − 18.2 = 61.8 litre at 3 atm, T l ​ = n R P V ​ = 1389 K. Q = n C v ​ ( T l ​ − 300 ) + W o n ​ = 40.5 kJ.

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