Question

Rebelmatk Cycle bewo Veas 3) The Diesel... .I mean, Rebelmatic engine is used in vehicles across the globe. A diatomic, ideal gas (γ 7/5) undergoes adiabatic compression from point 1 (Vii P), followed by isobaric expansion as the fuel is burned, then adiabatic expansion to point 4, and finally the pressure is released at constant volume back to point 1. a) The compression ratio for this engine is Vi/V2 18, what is the ratio of the temperatures 72 and Ti and the pressures P2 and P? b) If the system starts at point 1 with 0.1 mole of gas at atmospheric pressure (P 1.01 × 105Pa) and an ambient ternperature of 300K, what is the volume of the gas at point 2? b) The fuel is injected and burns to maintain a constant pressure to point 3, where the volume is now 3V2. What is the heat that is added to the system in this portion of the cycle?

Answer 1

3. for the diesel engine

gamma = 1.4

1-2 Adiabatic compression

2-3 Isobaric Expansion

3-4 Adiabatic Expansion

4-1 Isochoric Cooling

a. V1 = V

P1 = P

then for adiabatic compression

P1V1^1.4 = P2V2^1.4

P1/P2 = (V2/V1)^1.4 = (1/18)^1.4 = 0.017483102

also

P1V1 = nRT1

P2V2 = nRT2

T1/T2 = (P1/P2)(V1/V2) = 0.314695837

b. n = 0.1 mol

P1 = 1.01*10^5 Pa

T1 = 300 K

P1V1 = nRT1

V1 = 0.002468316 m^3

hence

V2 = V1/18 = 1.371287*10^-4 m^3

c. V3 = 3V2 = 4.1138*10^-4 m^3

for isobaaric expansion

heat supplied = Q = nCp(T3 - T2)

P3V3 = nRT3

P2V2 = nRT2

Q = nCp(V3 - V2)P2/nR

Cp - Cv = R

Cp/Cv = gamma

Cp - Cp/gamma = Cp(gamma - 1)/gamma = R

Cp = gamma*R/(gamma - 1)

Q = 1.4(2*1.371287*10^-4)*1.01*10^5/0.4*0.017483102

Q = 5545.3540738 J