Question

A gas in a piston–cylinder assembly undergoes a process for which the relationship between pressure and volume is pVn = constant. The initial pressure is 1 bar, the initial volume is 0.12 m3, and the final pressure is 9 bar. The value of the polytropic exponent is n = 1.9. Determine the final volume, in m3, and the work for the process, in kJ.

Answer 1

Answer:

The final volume is: 0.038 m3 adn the work for the process is: -24.42 KJ

Explanation:

The equation given for a polytropic process $P*V^{n}=C$ when n and C are constants. First we determine the C with the initial conditions:$100000*0.12^{1.9}=C= 1780$, we need to remember that 1 bar is the same to 100000 Pascals. Then we can calculate the final volume solving the equation given to:$Vfinal=\sqrt[n]{\frac{C}{Pfinal}}$ so we get:$Vfinal=\sqrt[1.9]{\frac{1780}{900000} } = 0.038(m3)$. Now using the integration for work:$Wb=\int\limits^2_1 {P}\,dV=\int\limits^2_1 {CV^{-n} } \, dV=C\frac{V2^{-n+1}-V1^{-n+1}}{-n+1} =\frac{P2*V2-P1*V1}{1-n}$, replacing data we find the work process like:$Wb=\frac{(900000*0.038)-(100000*0.12)}{1-1.9} =\frac{33977.46-12000}{-0.9} =-24419.4 (Joules)=-24.42 KJ$