Question

A stoichiometric mixture of ethanol (C₂H₆O), octane (C₈H₁₈), and air initially at T1 = 300 K, P1 = 100 kPa, P₂ =4500 kPa, and V1 = 5 liters (0.005 m³) is compressed in a piston-cylinder assembly in a polytropic process where n = 1.2

What is the final volume V₂ (m³ ), the initial total volume of moles (kmol), and the final Temperature T₂?

NOTE: Universal gas constant: Ru = 8.314 k]/ kmolK

Please show ALL steps and units with unit conversions.

Answer 1

For a polytopic process, PVⁿ = constant or P₁V₁ⁿ = P₂V₂ⁿ ...... eqn 1

and (P₁/P₂)^n-1/n = T₁/T₂ ......... eqn 2

From equation 2,

(100/4500)^0.2/1.2 = 300/T₂

So, T₂ = 566K

From equation 1,

100 × 0.005^1.2 = 4500 × V₂^1.2

or, V₂^1.2 = 3.85 * 10^-5

or, 1.2logV₂ = 3.85 * 10^-5

or, V₂ = 2.1 * 10^-4 m³

We know, n = P₁V₁/ RT₁

= 0.987 atm * 5 lit / (0.082 lit.atm.K^-1.mol^-1) . 300K ...... [100kPa = 0.98 atm]

= 0.2 mol