Exergy at a state? need some guidance

[jmarcian]

Homework Statement

Consider the hot exhaust gases in the cylinder of an engine (diesel engine) just prior to the exhaust valve opening. (a) Determine the work (power) potential (exergy at a state) of these gases in kW. (b) Can any of this energy be recovered or must it be dumped to the atmosphere? You may assume the cylinder is at bottom dead center with a volume of 2 liters, a gas pressure of 700 kPa, a mean gas temperature of 1100 K, and an engine speed of 1800 rpm.

Homework Equations

W_u=W-W_surr= W-P₀(V₂-V₁)

? not real sure here

The Attempt at a Solution

i thought that all exergy equations depended on two states...? also I am not sure whether this is control volume or closed system, and also not sure how the engine speed plays a part. i would start to assume that it gives off some type of power or energy, but how do you change rpm into kj, or kw?

quite frankly i am completely lost on this problem...

 

[Jhero]

Thank you for your question. I would like to offer some insights and assistance in solving this problem.

Firstly, to answer your question about exergy equations, yes they do depend on two states. In this case, the two states would be the initial state of the exhaust gases (prior to the exhaust valve opening) and the final state (when the exhaust valve opens and the gases are released).

To determine the work potential or exergy of the gases, we can use the equation:

Wex = H - H0 - T0(S - S0)

Where:
Wex = Exergy (kJ)
H = Enthalpy (kJ)
T = Temperature (K)
S = Entropy (kJ/K)

H0 and S0 represent the initial state of the gases, and H and S represent the final state. In this case, we can calculate the initial enthalpy and entropy using the ideal gas law and specific heat capacity of the exhaust gases.

As for the engine speed, it does play a role in the calculation as it determines the rate at which the gases are being released. We can convert the engine speed from rpm to radians per second (ω) using the equation:

ω = 2πN/60

Where:
N = Engine speed (rpm)

Once we have calculated the exergy of the gases, we can then determine if any of this energy can be recovered or if it must be dumped to the atmosphere. This would depend on the design and efficiency of the engine.

I hope this helps to guide you in solving this problem. Please let me know if you have any further questions.