Calculate Thermal Efficiency for a Diesel Cycle - Homework Help and Equations

[EngNoob]

Homework Statement

Calculate thermal efficiency for a diesel cycle, given the following.

P_1, P_2, P_3, P_4, V_1, V_2, V_3, V_4,

T_1, Specific Gas Constant, Specific Heat Capacity at constant pressure.

Homework Equations

Unsure, can't find notation for specific gas constant and specific heat capacity.

Thermal efficiency i think is heat in divided by heat out?

The Attempt at a Solution

I think to start i need to calculate T_2, T_3 and t_4. However i am unsure how and why i need to use the specific gas constant and the specific heat capacity?

I have calculate the work done for the pressure and volume points.

I have done loads of reading on this and managed to solve 90% of the problem, this is my final stage, however, i am not at a loss and have so many equations floating around my head i am dreaming of them.

Needed a.s.a.p to finish project.

Thanks for any help

 

[anathema]

you can give.





To calculate the thermal efficiency for a diesel cycle, you will need to use the following equation:

η = 1 - (T_4 - T_1) / (T_3 - T_2)

where η is the thermal efficiency, T_4 is the temperature at point 4, T_1 is the temperature at point 1, T_3 is the temperature at point 3, and T_2 is the temperature at point 2.

To calculate T_2, T_3, and T_4, you will need to use the following equations:

T_2 = T_1 * (P_2/P_1)^((γ-1)/γ)

T_3 = T_2 * (P_3/P_2)^((γ-1)/γ)

T_4 = T_3 * (P_4/P_3)^((γ-1)/γ)

where γ is the ratio of specific heats, which can be calculated using the following equation:

γ = specific heat capacity at constant pressure / specific gas constant

You will need to use the specific gas constant and specific heat capacity at constant pressure for the gas being used in the diesel cycle. These values can be found in a thermodynamics textbook or online.

Once you have calculated T_2, T_3, and T_4, you can plug them into the first equation to calculate the thermal efficiency. Remember to use the same units for all temperatures and pressures.

I hope this helps and good luck with your project.

 

[Moetasim]

provided


I would suggest starting by clarifying the given information and equations. It would be helpful to know the units for the given pressures and volumes, as well as the specific gas constant and specific heat capacity. These values will be necessary for accurate calculations.

Once the units are clarified, the first step would be to calculate the temperatures at each point using the ideal gas law (PV = nRT) and the given values for pressure, volume, and temperature. Then, using the specific heat capacity at constant pressure, you can calculate the heat added at each stage of the cycle.

To calculate the thermal efficiency, you will need to know the heat input and heat output. The heat input can be calculated as the difference between the heat added at the first stage (Q1) and the heat rejected at the final stage (Q4). The heat output can be calculated as the work done during the cycle, which can be found by integrating the pressure-volume curve.

Once you have both the heat input and heat output, you can calculate the thermal efficiency as heat output divided by heat input. This will give you a percentage value representing the efficiency of the diesel cycle.

It is important to double-check your calculations and make sure they are consistent with the equations and principles of thermodynamics. If you are still struggling, seeking clarification from a professor or classmate may also be helpful. Good luck with your project!