Problem 1.4

A chamber with kg of air at an initial temperature and pressure of ^oC and kPa undergoes an isentropic process, the final temperature attained being ^oC. Find the final pressure, the initial and final densities, and the initial and final volumes.

Given:

To calculate: $ p_{2}=? $, $ \rho_{1}=? $, $ \rho_{2}=? $, $ v_{1}=? $, $ v_{2}=? $.

Using isentropic relation, with $ \gamma=1.4 $ for air,

$$ \frac{p_{2}}{p_{1}}=\left(\frac{T_{2}}{T_{1}}\right)^{\gamma/\left(\gamma-1\right)} $$ $$ p_{2}=p_{1}\left(\frac{T_{2}}{T_{1}}\right)^{\gamma/\left(\gamma-1\right)} $$

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The density $ \rho_{1} $ can be calculated using the ideal gas equation as,

The density $ \rho_{2} $ can be calculated using the ideal gas equation as,

Since the mass is constant , the volumes can be calculated as,

Problem 1.4:

Solution: