Temperature Estimation for Compressed Air in an Internal Combustion Engine

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In estimating the temperature of compressed air in an internal combustion engine, the initial conditions are atmospheric pressure and 20 degrees C, with a compression ratio of 8.0 leading to a final pressure of 38 atm. The user attempted to apply the ideal gas law (pv = nRT) to find the final temperature but received incorrect results. They also mentioned another equation related to volume change, suggesting that the original volume may not be necessary for the calculation. The final temperature should be calculated by adding the change in temperature to the original temperature. Clarification on the appropriate equations and methods is sought for accurate results.
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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
\Deltav = \betaVo\DeltaT

\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.
 
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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
 
Last edited:
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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