Question

8. Consider air that is conteined within an air tight cavity surrounded by a large metal enclosure and piston, The metal always has & temperature of 300 K. Assume that the gas within the csvity always comes into thermal equilibrium with the metal enclosure. The gas constants are γ-14, R-287 Nm/kg K and de-1006 J/kg K. air The air in the cavity has an initial denaity 1 kg/m3 and temperature 300 K. Calculate thea numerical values of the changes in P, p, T, e and h when the volume of the cavity is decreasod to half of the original volume.

Answer 1

Since the air is in thermal equilibrium even after the compression, the final temperature of air remains the same as before. T = 300 K

The process is like an isothermal process. So pressure doubles as does the density.

Also the change in e and h is also 0.

Initial pressure is given by

$P=\rho RT$

$P=1\times287\times 300=86100\textup{ Pa}$

So that the final pressure is

$P_f=172200\textup{ Pa}$