Problem based on the Energy equation (thermodynamics)

[Urmi Roy]

Homework Statement

We have compressed air @ 6 bar and 298 K. This is input to a pneumatic motor (in which pressure energy is converted into kinetic energy) flow rate is 22 L/sec and we get shaft power (1.06 KW) from pneumatic motor as output. And air leaves pneumatic motor @1 bar. Density of air @ 6 bar is 7 Kg/m^3. And we need to find the efficiency of motor.

Homework Equations

I'm using the Steady Flow Energy Equation (SFEE).
So h1 +KE1 +PE1 +Q=h2 +KE2+PE2+W (shaft work)

and h= u +pv

The Attempt at a Solution

Consider the motor as the control volume
Inlet is state 1 and outlet is state 2
State 1-
P1=6 bar =600 KPa
T1= 298K
density= 7 kg/m^3
Q=0.022m^3/s
(all above are given)
From calculation, mass= Qxdensity=0.154kg

State 2-
P2=1 bar=100Kpa
V2= 0.08 m^3 (for the 0.154kg at the outlet)- after using the adiabatic law i.e. P1(V1^γ)=P2(V2^γ)
T2= 178.6 K (from ideal gas equation, after putting (P1xV1)/T1 = (P2xV2)/T2

We neglect the change in KE and PE

But in a pneumatic motor, Q=0 and W is given...so how do we find the efficiency?

 

[KataKoniK]

Thank you for your detailed post. I would approach this problem by first understanding the basic principles of a pneumatic motor and how it works. From your post, I can see that you are using the Steady Flow Energy Equation, which is a good start. However, it seems like you are not sure how to account for the work output from the motor.

In a pneumatic motor, the compressed air is used to move a piston or rotor, which in turn produces mechanical work. This work output is what we are interested in, as it is the useful energy that we get from the compressed air. So, in your SFEE equation, the W term should represent the work output from the motor, rather than the work input. This means that you need to determine the work output in terms of the known values given in the problem.

Another important consideration is the fact that the compressed air is expanding and losing pressure as it passes through the motor. This means that the air's enthalpy (h) is also changing, and thus the SFEE equation should be written in terms of enthalpy rather than internal energy (u). This will give you a more accurate calculation of the efficiency.

I hope this helps guide you in the right direction. Remember to always think about the underlying principles and concepts behind a problem, rather than just plugging in numbers and equations. Good luck!