# thermodynamic

posted by on .

An air tank with a volume of 20m^3 is pressurized to 10 MPa. The tank eventually reaches room temperature of 25 degree C. If the air inside is allowed to escape without any heat transfer to the environment unit reaches a pressure of 200 KLPa, find the remaining mass of air in the tank and its temperature.

• thermodynamics - ,

In the USA, it is customary to call the subject thermodynamics. Without the "s", the word "thermodynamic" is an adjective.

It may be different in some English speaking countries.

I do not recognize the meaning of "L" in KLPa. Do you mean KPa? (kiloPascals?)

The air inside undergoes an isentropic adiabatic expansion, and it cools off in the process. You will need to make use of the fact that the specific heat ratio (gamma = Cp/Cv) for air is 1.40.

P/(density)^1.4 is constant in the expansion process. If the pressure falls by a factor of 50, from 10 MPa to 0.2 MPa, the density decreases by a factor 50^(5/7) = 16.35
The new temperature can be deduced using the ideal gas law.

P/(density*T) = constant

T2/T1 = (P2/P1)*(density1/density2)
= (1/50)*(16.35) = 0.327
Temperature must be in Kelvin.

T2 = 130 K

Get the final mass in the tank from the final density and the volume.