Question 4.22: Problem: An evacuated cylinder is connected to a pipeline ca...
Problem: An evacuated cylinder is connected to a pipeline carrying compressed air at 300 kPa and 52 °C. The cylinder fills until its pressure is the same as that in the pipeline. Determine the final temperature in the tank.
Find: Final temperature T_2 in the tank.
Known: Inlet pressure P_1 = 200 kPa, inlet temperature T_1 = 52 °C = 325.15 K, final pressure P_2 = 300 kPa.
Assumptions: Air is an ideal gas, there are no heat losses from the cylinder, no changes in kinetic or potential energy of the cylinder.
Governing Equation:
Energy balance \Delta U=Q + W + m_1h_1 – m_2h_2
\Delta U= m(u_2 – u_1)=\underbrace{Q}_{=0} + \underbrace{W}_{=0} + m_1h_1 – m_2h_2
Where u_1 and u_2 are the initial and final specific internal energies of the gas in the cylinder and m is the final mass of air in the cylinder. There is no exit from the system, so m_2 = 0. The cylinder was initially evacuated so u_1 = 0. The final mass in the cylinder equals that which entered, so m = m_1 . Therefore,
u_2 = h_1 .
From the definition of enthalpy, h_1 = u_1 + P_1 \nu _1 where P_1 \nu_1 is the flow work. The final internal energy of the air in the cylinder equals the internal energy of the air in the pipeline plus the work done in filling the cylinder.
Using the ideal gas table (Appendix 7), for a temperature of 325 K (since inlet temperature is 325.15 K), h_1 = 325.31 kJ / kgK. Therefore, u_2 = 325.31 kJ / kgK. Using this value and interpolating in the ideal gas table for air,
T_2 = 453.8 \ K.
Answer: The final temperature of the cylindrical tank is 454 K.