# Question: it is necessary to estimate how rapidly a piece of...

###### Question details

It is necessary to estimate how rapidly a piece of equipment can be evacuated. The equipment, which is 0.7 m^3 in volume, initially contains carbon at 340 K and 1-bar pressure. The equipment will be evacuated by connecting it to a reciprocating constant-displacement vacuum pump that will pump out 0.14 m^3 /min of gas at any conditions. At the conditions here carbon dioxide can be considered to be an ideal gas with Cp = 39 J/mol K. What will be the temperature and pressure of the carbon dioxide inside the tank after 5 minutes of pumping if there is no exchange of heat between the gas and the process equipment?

We know that the system is open unsteady-state and that the energy balance simplifies to (Cv/R)ln(T2/T1)=ln(n2/n1) which is also (T2/T1)=(P2/P1)^(R/Cp)

The mass balance gives us n2=n1-n(out)

We also know that mass and density is a function of time and we think that we need to write the mass as a differential function of time in order to solve for mass after 5 min. However, we dont know how to mass in the differential form. Please help! Pretty sure the answer is close to T2=259.3 K and P2=0.28 bar