What Is the Temperature of Compressed Air in a Diesel Cylinder?

[Karol]

Homework Statement

At the start of the compression stroke, the cylinder in a diesel motor contains 300[cm³] of air at atmospheric pressure and 27⁰C, and at the end of the stroke the volume is 20[cm³] and manometric pressure 41[atm]. What is the temperature.

Homework Equations

$$PV=nRT\rightarrow \frac{P_1V_1}{T_1}={P_1V_2}{T_2}$$
In an adiabatic process: $T_1V_1^{\gamma-1}=T_2V_2^{\gamma-1}$
And: $P_1V_1^{\gamma}=P_2V_2^{\gamma}$
γ for air=1.4

The Attempt at a Solution

First i check if this is an adiabatic process by comparing the initial and final volumes and pressures:
$$T_1V_1^{\gamma-1}=1\cdot 300^{1.4}=2937$$
$$T_2V_2^{\gamma-1}=42\cdot 20^{1.4}=2784$$
So it's not, heat leaks.
So i calculate using the equation of state:
$$\frac{P_1V_1}{T_1}={P_1V_2}{T_2}\rightarrow \frac{1\cdot 300}{300}=\frac{42\cdot 20}{T_2}\rightarrow T_2=840^0K$$
Is my method true?

 

[Chestermiller]

Yes. Note that this is strictly an ideal gas problem. You didn't need to use the equations with the gammas. But, if you had, would your results have been consistent with the gamma equations?

Chet

 

[Karol]

But, if you had, would your results have been consistent with the gamma equations?

You mean if i solved the gamma equations? i guess not since it isn't adiabatic, i don't understand the question, i think

 

[Chestermiller]

You mean if i solved the gamma equations? i guess not since it isn't adiabatic

Yes, that's what I meant, and your conclusion is correct.

Chet