Answer to Question #271824 in Molecular Physics | Thermodynamics for MaTMaT

Question

an isentropic compression process, air is compressed to an initial pressure of 100 psi to 200 psi. What is the final volume in cubic inches if the initial volume is 10 in^3?

Answer 1

Given:

$\gamma=1.4$

$P_1=100\:\rm psi$

$P_2=200\:\rm psi$

$V_1=10\:\rm in^3$

The equation of an isentropic (adiabatic) processes is given by

$$P_1V_1^{\gamma}=P_2V_2^{\gamma}$$

So

$$V_2=V_1 \left(\frac{P_1}{P_2}\right)^{1/\gamma}$$

$$V_2=10 \left(\frac{100}{200}\right)^{1/1.4}=6.1\:\rm in^3$$