# Thermodynamics: Otto Cycle

## Homework Statement

Analyze an air-standard Otto cycle assuming it is a cold cycle with properties evaluated at 300 K. Air intake and exhaust are at 300 K, 1 bar. After the combustion (heat in) process, the temperature is 2500K. The compression ratio is 9. The volume at bottom dead center is 1 liter.

a. What is the mass of air in the cycle?

b. How much work is produced during expansion?

c. How much work is consumed during compression?

d. How much energy is transferred into the air during heating?

e. What is the thermal efficiency of the cycle?

## Homework Equations

The biggest problem I am having is identifying which temperature and pressure corresponds to what process. Does air intake and exhaust mean that T1 = 300K?

1 to 2: Isentropic Compression (BDC to TDC)
2 to 3: Constant Vol. heat transfvr to air while piston at TDC.
3 to 4: Isentropic expansion
4 to 1: Constant Vol. where heat rejected from air at BDC

Also, I can do c,d,e once a and b are known, but I need help with those.

## The Attempt at a Solution

b) efficiency of turbine n_t = (h1-h2)/(h1-h2s)
h2 = h1 - n_t(h1-h2s)
= 2804.2 -0.75(2804.2 - 2084.63) = 2264.5225
Power of pump Wp_dot = m_dot*(h4-h3)
h4 = h3 + Wp_dot/m_dot = h3 + v3(p4-p3)/n_p

Where n_ p = pump efficiency
h = enthalpy
p = pressure
m_dot = mass flow rate
v = specific volume

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Just a few questions for you to think about (well and for me to know where you are)

Have you drawn the cycle out on paper?
Remember this is air standard - so what equations are you using?
Why are you using a turbine in your attempt at a solution?
Why are you using a mass flow rate - what type of system is an otto cycle?
Remember cycle efficiency is not the same as component efficiency.

Think about these and let me know what you think.

Yeah I have it drawn out on paper.

For air standard: W_12 = u2 -u1
W_34 = u3-u4
Q_23 = u3-u2
Q_41 = u4-u1
Thermal efficiency n = 1 - [(u4-u1)/(u3-u2)]
For isentropic processes: v_r2 = (V2/V1)*v_r1
v_r4 = (V4/V3)*v_r3
where v_r is the reduced specific volume, which i can use to get the temperature and specific internal energy
For constant Volume: p3 = p2*(T3/T2)
p4 = p1*(T4/T1)

In my book, the cycle consists of a pump, boiler, turbine, and condenser. I am using n_t to get h2.

Isnt the mass flow rate constant throughout the process?

A pump,boiler, turbine, and condenser is a Rankine/Carnot cycle that typically tuns on steam.

The Otto cycles are the 4 stroke spark ignition cycle that can have an air standard equivilant.

There is a rather major fundamental mistake in something here because you are trying to solve a completely different cycle than you have the information for. Some of your equations are based on the ideal gas law and some are based on steam cycle principals.

http://en.wikipedia.org/wiki/Otto_cycle#The_Otto_cycle
http://en.wikipedia.org/wiki/Rankine_cycle

If this doesnt solve your problems I would suspect that there is something majorly wrong with the question (info) could you give scan of it?

Oh sorry, my mistake. You were right. I typed in something i didnt meant to. The question is correct. I am still having trouble determining which is which temperature, pressure, etc...
Here are my attempts:

Assuming T1 = 300K, u1 = 214.07 kJ/kg, v_r1 = 621.2

Then v_r2 = v_r1/r = 69.02

Interpolating: T2 = 702.75 K, u2 = 514.5 kJ/kg

mass m = (p1*V1)/[(R/MW)T1] = 1.16g, R = 8.3145

W_cycle = m[(u3-u4) - (u2-u1)], need u3 and u4

T2/T1 = (V1/V2)^(k-1), k= 1.4

V2 = 0.00499 L

p2 = p1[(T2*V1)/(T1*V2)] = 1670.676 bar
p3 = p2(T3/T2)

The internal energy can be found from CvT (specific heat at const vol)

and Cp/Cv = k

This would allow you to find Q in by m*cv*delta_T

and this in turn would allow you to find u3 as you know u2.

EDIT: This is all from memory and ive not done this in quite a while so I may be wrong.

I believe this stuff is in Thermodynamics - cengel and boles. I dont have my books with me so I cant check.

Also I think your V2 value is a bit off which is giving you the incorrect pressures for p2 and p3. [Vmax/Vmin is Rc]

Last edited:
What would be by T1,T2,T3, and T4?

plz tell me how to interpolate in otto cycle to find temperature

Redbelly98
Staff Emeritus