# Temperature drop when expanding heated compressed air

1. Dec 3, 2012

### Inventrius

1. The problem statement, all variables and given/known data

I need to know how much the temperature drops after an inline heater which heats an airflow of 5 lbs/min up to 88 °C with an pressure of 54 PSI. When the air exits the heater it is released into the free air where it is 20 °C.

I know that the air will expand to a bigger volume then, which will lead to a temperature drop. So I need to know how much this drop will be.

2. Relevant equations

P1 * V1^γ=P2 * V2^γ

T1 * V1^(γ-1)=T2 * V2^(γ-1)

3. The attempt at a solution

γ= 1.4
V1= 5 lbs = 1.853 m3
T1= 88 °C = 361 K
P1= 54 PSI = 3723163.9

P2= 101325 Pa
V2= ?
T2= ?

P1 * V1^γ=P2 * V2^γ
V2 = 4.69447 m3

T1 * V1^(γ-1)=T2 * V2^(γ-1)
T2 = 248 K

This will say that the temperature decreases to -25 °C which sounds like a wrong answer in my opinion.

I also thought to use the ideal gas law with --> P*V= m*Rs*T
But I dont know how I should use it in my case..

Anybody who can give me a solution?