Isenthropic compression 5000L, 5Bar, 2500L, 288K

[dbag123]

Homework Statement

Container has 5000L of air at 5 Bar How does the pressure, temperature and density change when the air is compressed to half.

Relevant Equations

P1*V1/T1=P2*V2/T2

Hello

Pressure by P2=P1*V1/P2 which comes out to 10 Bar

Density by P/Rd/T which comes out to 12,09 Kg/M³

according to the homework equation T2 would equal 144K, but if you compress air does it not heat up?

 

[Andrew Mason]

You have to apply the adiabatic condition: $PV^{\gamma} = K$ where $\gamma = \frac{C_P}{C_V} = 7/5 = 1.4$. That will give you the final pressure and from that you can determine the final temperature using the ideal gas law.

AM

 

[dbag123]

what do the C_p and C_v stand for?

 

[Andrew Mason]

what do the C_p and C_v stand for?

... Heat capacities of air at constant pressure and constant volume, respectively.

AM