Temperature drop when expanding heated compressed air

[Inventrius]

Homework Statement

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.

Homework Equations

P1 * V1^γ=P2 * V2^γ

T1 * V1^(γ-1)=T2 * V2^(γ-1)

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 don't know how I should use it in my case..

Anybody who can give me a solution?

 

[KataKoniK]

To calculate the temperature drop, we need to use the ideal gas law, which is P*V = n*R*T, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature. Since we are dealing with air, we can assume that the number of moles and the gas constant remain constant. Therefore, we can rearrange the equation to solve for temperature: T = P*V/(n*R).

First, we need to convert the given values to SI units. The pressure is given in PSI, so we need to convert it to Pascals (Pa). 1 PSI is equal to 6894.76 Pa, so the pressure is actually 3723163.9 Pa. The volume is given in pounds (lbs), so we need to convert it to kilograms (kg). 1 pound is equal to 0.453592 kg, so the volume is actually 0.83817 kg.

Now we can plug in these values into the equation: T = (3723163.9 Pa)*(0.83817 kg)/((1 mol)*(8.314 J/mol*K)) = 346 K.

Since the air is being heated to 361 K and then cooled to 346 K, the temperature drop is 361 K - 346 K = 15 K. We can also convert this to Celsius by subtracting 273.15 from both temperatures, giving us a temperature drop of approximately 15 °C.

In conclusion, the temperature drops from 88 °C to 73 °C after the air exits the heater and expands into the free air. This is a significant drop, so it is important to consider the effects of temperature changes on the performance of the system.