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## Homework Statement

At the start of the compression stroke, the cylinder in a diesel motor contains 300[cm

^{3}] of air at atmospheric pressure and 27

^{0}C, and at the end of the stroke the volume is 20[cm

^{3}] 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?