Temperature Estimation for Compressed Air in an Internal Combustion Engine

[cubixguy77]

Homework Statement

In an internal combustion engine, air at atmospheric pressure and a temperature of about 20 degrees C is compressed in the cylinder by a piston to (1/8) of its original volume (compression ratio 8.0).

Estimate the temperature of the compressed air, assuming the pressure reaches 38 atm.

Homework Equations

pv = nRt
$$\Delta$$v = $$\beta$$Vo$$\Delta$$T

$$\beta$$ = .0034 for air

The Attempt at a Solution

If i let p1 * v1 / T1 = p2 * v2 / T2
i can make the associations and end up with T2 = T1 * 38 / 8
however this result is incorrect.
note that i used pv = nRt for this result, I'm not sure if the other equation should be used or not,
i've only gotten garbage answers using it thus far.

Any help would be much appreciated,
Thanks.

 

[ptr]

Try using the other equation you have, though I know not what it is, and then, $$\Delta V = (1-\frac{1}{8}) V_0$$, from which it seems that the original volume is not here required.

-the final temperature is the change in temperature plus the original temperature

 

[thomate1]

I would like to clarify a few things before providing a response. Firstly, it is important to note that the given problem does not specify the type of internal combustion engine or its operating conditions. Therefore, any temperature estimation will be an approximation and may vary depending on the specific engine design and operating parameters.

That being said, the ideal gas law (pv = nRT) can be used to estimate the temperature of the compressed air in the engine cylinder. However, it is important to note that this equation assumes that the gas is in a state of thermodynamic equilibrium, which may not be the case in a rapidly changing internal combustion engine.

Using the given information, we can calculate the initial pressure (p1) and volume (v1) of the air before compression. We know that the compression ratio (r) is 8, so the final volume (v2) can be calculated as v2 = v1/r. We also know that the final pressure (p2) is 38 atm. Plugging these values into the ideal gas law, we get:

p1v1/T1 = p2v2/T2

Solving for T2, we get:

T2 = (p1v1T1)/(p2v2)

Substituting the values, we get:

T2 = (1 atm * v1 * 293 K)/(38 atm * v1/8)

Simplifying, we get:

T2 = 244 K

Therefore, the estimated temperature of the compressed air in the engine cylinder is approximately 244 K or -29 degrees Celsius.

However, as mentioned earlier, this is just an approximation and the actual temperature may vary depending on the engine design and operating conditions. Additionally, the assumptions made in using the ideal gas law may not accurately reflect the real-world conditions in an internal combustion engine. Further analysis and experimentation would be needed to obtain a more accurate estimation of the compressed air temperature.