# Homework Help: Adiabatic compression of air

1. Sep 6, 2010

### rg2004

I'd just like to check my answer, it seems too big

1. The problem statement, all variables and given/known data
Air initially at 20◦C is compressed by a factor of 15.

What is the final temperature assuming that the compression is adiabatic and $$\gamma$$ ≈ 1.4 the value of $$\gamma$$ for air in the relevant range of temperatures? By what factor does the pressure increase?

2. Relevant equations

PV$$\gamma$$=constant
TV$$\gamma$$-1=constant

3. The attempt at a solution

V1/15=V2
T1V1$$\gamma$$-1=T2V2$$\gamma$$-1
293.15*V1$$\gamma$$-1=T2*V1/15
293.15*15$$\gamma$$-1=T2
293.15*15.4=T2
T2=866.017 kelvin

P1V1$$\gamma$$=P2V2$$\gamma$$
P1V1$$\gamma$$=P2V1/15$$\gamma$$
P1*15$$\gamma$$=P2
thus P2 increased by a factor of 44.31

does it look right?

2. Sep 6, 2010

### Andrew Mason

Looks right. You can also use the ideal gas law to find final pressure:

$$nR = P_1V_1/T_1 = P_2V_2/T_2$$

$$P_2/P_1 = T_2V_1/T_1V_2 = \frac{866*15}{293} = 44.3$$

AM

3. Sep 6, 2010

Thanks!