Air in the cyclinder of a diesel engine is compressed to `1/15` of its initial volume. If initial temperature is `300K` and initial pressure is `10^(5)Pa`, find the final temperature and final pressure. Take `gamma= 1.4`.

Explanation

To solve the problem, we will use the principles of adiabatic processes in thermodynamics. The key equations we will use are:

1. For an adiabatic process:
\[ P_1 V_1^\gamma = P_2 V_2^\gamma \]
2. The relationship between temperature and volume in an adiabatic process:
\[
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