How Is Work Calculated in a Diesel Engine Thermodynamic Cycle?

[EngNoob]

Homework Statement

Engine data for a heat engine cycle, ie: Diesel.

State ...|...1...|...2...|...3...|...4...|
Pressure(Pa) | 1x10^5 | 11.764x10^5 | 11.764x10^5 | 2.207x10^5 |

Volume(m^3) |. 0.826 .|... 0.142 ...|... 0.25 ...|... 0.826 ...|

The gas has a compression and expansion index of 1.4,

determine the work done in (kJ) in the cycle.

Homework Equations

I am not sure. But to have an attempt i would say.

Constant Volume: W = 0

Constant Pressure: W = P(V_2 - V_1)

Constant Tempreture: W = P_2 * V_2 * ln (V_2/V_1)

The Attempt at a Solution

I have done a P-v diagram, and came up with.

1-2: Istothermal (Constant Tempreture)
2-3: Isobaric (Constant Pressure)
3-4: Isothermal (Constant Tempreture)
4-1: Ischoric (Constant Volume)

I am unsure about

1-2 and 3-4 as it could be a polypropic process (Temp/Press/Vol Change) but i think this has to do with the exp/comp index? but not sure how to figure out?

I came up with

-30431.859(kJ)

I think this is wrong, as this would indicate mins work.

Do i need to convert PA to KPA or MPA?

I would welcome any help, advice, or some hints/tips.

 

[EngNoob]

Any Ideas Anyone? Would really appreciate it, a very lot.

Does anyone know the Notation for the expansion and compresion index?

 

[Moetasim]

Based on the data provided, it appears that the engine is operating through a four-stroke cycle, which is commonly used in Diesel engines. The four strokes are intake, compression, power, and exhaust. In the intake stroke, the piston moves down and draws in a mixture of air and fuel into the cylinder. In the compression stroke, the piston moves up and compresses the mixture, increasing the pressure and temperature. In the power stroke, the mixture is ignited by the spark plug, causing a rapid expansion of gases and pushing the piston down. Finally, in the exhaust stroke, the piston moves up and pushes the remaining exhaust gases out of the cylinder.

To calculate the work done in this cycle, we can use the first law of thermodynamics, which states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system. In this case, we can assume that the heat added to the system is equal to the work done by the engine, as there is no other source of energy being added or removed.

Using the equations you have provided, we can calculate the work done in each stroke of the cycle. In the intake stroke (1-2), the volume is increasing at a constant pressure, so the work done is given by W = P(V_2 - V_1). In the compression stroke (2-3), the volume is decreasing at a constant temperature, so the work done is given by W = P_2 * V_2 * ln (V_2/V_1). In the power stroke (3-4), the volume is increasing at a constant temperature, so the work done is given by W = P_2 * V_2 * ln (V_2/V_1). And in the exhaust stroke (4-1), the volume is constant, so the work done is zero.

To calculate the work done in the entire cycle, we need to sum up the work done in each stroke. This will give us the net work done by the engine. Since we are given the pressures and volumes at each state, we can plug them into the equations and calculate the work done. However, we also need to consider the compression and expansion index of the gas, which is given as 1.4. This index represents the ratio of specific heats for the gas, and it affects the calculation of work done in the compression and expansion strokes.

Without going through the