Question

In a cylinder of an automobile engine, immediately after combustion the gas is confined to a volume of 46.0 cm3 and has an initial pressure of 3.10 106 Pa. The piston moves outward to a final volume of 300 cm3, and the gas expands without energy transfer by heat. (Assume the gas in the engine is diatomic with γ = 1.40.)

(a) What is the final pressure of the gas? kPa

(b) How much work is done by the gas in expanding? J

Answer 1

V1 = 46 cm^3, V2 = 300 cm^3, P1 = 3.1*10^6 Pa, γ = 1.40

(a) in adiabatic process PV^γ = constant

(V1/V2)^γ = (P2/P1)

(46/300)^1.4 = (P2/(3.1*10^6))

P2 = 2.2452*10^5 Pa

(b) Work don in adiabatic process

W = (1/γ-1) (P1v1 -P2V2)

W = (1/0.4) (3.1*10^6*46*10^-6 - 2.2452*10^6*300*10^-6)

W = -1327.4 J