Explanation:
Let inlet flow rate = [tex]q_{1}[/tex]
and, outlet flow rate = [tex]q_{2}[/tex]
Also, it is known that [tex]q_{2} - q_{1}[/tex] = [tex]\frac{dn}{dt}[/tex] ....... (1)
where, n = number of moles accumulating in tank
According to ideal gas equation, PV = nRT
Hence, P = [tex]\frac{nRT}{V}[/tex]
[tex]\frac{dP}{dt}[/tex] = [tex](\frac{RT}{V}) \frac{dn}{dt}[/tex]
[tex]\frac{dn}{dt}[/tex] = [tex](\frac{V}{RT}) \frac{dp}{dt}[/tex]
As it is given that T and V are constant. Hence, from equation (1) and (2) we get the following.
[tex]q_{2} - q_{1}[/tex] = [tex](\frac{V}{RT}) \frac{dp}{dt}[/tex]
[tex]\frac{dp}{dt}[/tex] = [tex]\frac{RT}{V} q_{2} - q_{1}[/tex]
