Final Temperature and Pressure Increase in Adiabatic Air Compression?

[rg2004]

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

Homework Statement

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?

Homework Equations

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

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 kelvinP₁V₁^\gamma=P₂V₂^\gamma
P₁V₁^\gamma=P₂V₁/15^\gamma
P1*15^\gamma=P2
thus P2 increased by a factor of 44.31does it look right?

 

[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

 

[rg2004]

Thanks!