Air is compressd in a cylinder

1. Jan 5, 2015

Karol

1. The problem statement, all variables and given/known data
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.

2. Relevant 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

3. 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?

2. Jan 5, 2015

Staff: Mentor

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

3. Jan 6, 2015

Karol

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

4. Jan 6, 2015

Staff: Mentor

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

Chet