Question

A) A tank with volume 5m^3 is to be pressure tested before use. Tank is going to be filled with a 30 bar source at 20 C (degrees Celsius)and tested to 15 bar . Assume no heat transfer to or from the surroundings, what is the temperatue of the gas after the filling process if the tank orignially contained air at 1 bar and 20C (Celsius). Assume Ideal Gas with Cp= 3.5R

B) after some very long time has passed, the temperature in the tank returns to the ambient temperature. what is the new pressure in the tank?

Answer 1

a) as per the data provided there is no heat transfer between system and surrounding. Hence the process is an adiabatic process

T1 = 20oC = 293.15 K

P1 = 1 bar

P2 = 30 bar

For an adiabatic process

Now Cp = 3.5 R

and we know that

Cp -Cv =R

Cv = Cp- R = 3.5 R -R = 2.5 R

Cp/Cv = 35/2.5 = 1.4

we will substitute all data in the above equation

T2 = 689.9422 K

B) we will use following relation from ideal gas

(P1*V1/T1) = (P2*V2/T2)

Now T1 = T2

and also the volume occupied by the gas will be same as the tank and since tank is not allowed to let out of the tank the Volume will remain unchanged

V1 = V2

Hence P1 =P2

Hence pressure should be 1 bar when the temperature has been brought back to normal room temperature