# Temperature of Compressed Air

## Main Question or Discussion Point

Hello,

We all know that if you compress air the pressure and temperature increase together.

But how can I calculate the relationship?

For example: What pressure (psi) do I need to compress air to so it is 100degC?

Many Thanks,

Matthew.

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mgb_phys
Homework Helper
The equation is PV = nRT
P = pressure
V = volume
T = temperature
n = the amount of gas, if you don't ad or remove any you can ignore this.
R = a constant to get all this in the correct units.

So basicaly PV/T is the same before and after and as long as you use the same units it all works.
Remember to do this in terms of changes in temperature. If you want this in absolute temperature you need to convert to Kelvin (google absolute temperature)

In Thermodynamics there are different fundamental THERMODYNAMIC PROCESSES namely Isobaric, Isthermal, Isentropic, and Polytropic and Isochoirc processes.

Each of these processes has its own unique method of heating or cooling of the air/gas depending on the boundary conditions or type of surrounding or keeping some fundamenrtal parameters like pressure, tempreature, volume or entropy a constant.

Depending on the typr of process chosen the values and relations between the pressure, tempreature ( as menioned in your case) will vary.

The basic equation is the Ideal Gas Equation PV = mRT which remains applicable in all cases in any process.

But there are another set of eqautions derived from the above ie PV^n = C, where n is called the polytropic index, and all the above processes have a particular value of n. And depending on this value of n for each process the amopunt of heat or pressure required to heat up or compress air to a particular value will depend on or vary.

It all depends on your choice of process and the variables will change according to the particular equation.

The equation is PV = nRT
P = pressure
V = volume
T = temperature
n = the amount of gas, if you don't ad or remove any you can ignore this.
R = a constant to get all this in the correct units.

So basicaly PV/T is the same before and after and as long as you use the same units it all works.
Remember to do this in terms of changes in temperature. If you want this in absolute temperature you need to convert to Kelvin (google absolute temperature)
OK, this is true for isothermal condition. For an adiabatic system, the temperature increases when you compress air. I should think there is a relation between the temp rise and pressure ratio (before and after compressing)

pixel01 - you have the right idea.

i have found this, which is what I am trying to do. I just need to know the psi required for 100degC rather than 1000degC. Can anyone help change the equation?

*********
QUESTION

What compression ratio Vmax / Vmin will raise the air temperature from 20C to 1000C in an adiabatic process?

the gas is diatomic

For an adiabatic process, with Q = 0, the first law of thermodynamics is:

Change in thermal energy = Work. Compressing a gas adiabatically (W > 0) increases the thermal energy. So an adiabatic compression raises the temperature of a gas.

Pf = Pi(Vi/Vf)^gamma

gamma = 1.40 for a diatomic gas (like air)

Pf = Pi(Vmax/Vmin)^1.40

Wait a minute:

(Tf) Vf^(gamma - 1) = (Ti) Vi^(gamma - 1)

(1,273K)Vf^(gamma-1) = (293K)Vi^(gamma -1)

(1,273K) Vf^0.4 = (293K) Vi^0.4

1,273K / 293K = Vmax^0.4/Vmin^0.4

4.3447 = (Vmax^0.4 / Vmin^0.4)

(4.3447)^2.5 = (Vmin^0.4 / Vmax^0.4)^2.5

Vmax/Vmin = 39.346

So you would need to increase pressure to 2,513 psi if you started from atmospheric pressure.

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