Question

Air is to be compressed so that its volume is reduced to half of its original volume if the initial pressure is 200 kPa and the temperature is 20°C. Assume the ratio of specific heats is 1.4. Of the compression is done isentropically determine the required pressure.

Answer 1

Answer:

$P_{2} = 527.803\,kPa$

Explanation:

The politropic relationship for a isentropic process is:

$\frac{P_{2}}{P_{1}} = \left(\frac{V_{1}}{V_{2}} \right)^{\gamma}$

Where $\gamma$ is the ratio of specific heats

The final pressure is:

$P_{2} = P_{1}\cdot \left(\frac{V_{1}}{V_{2}}\right)^{\gamma}$

$P_{2} = (200\,kPa)\cdot (2)^{1.4}$

$P_{2} = 527.803\,kPa$