Natural gas, with the thermodynamic properties of methane, flows in an underground pipeline of \(0.6 \mathrm{~m}\) diameter. The gage pressure at the inlet to a compressor station is \(0.5 \mathrm{MPa}\); outlet pressure is 8.0 MPa gage. The gas temperature and speed at inlet are \(13^{\circ} \mathrm{C}\) and \(32 \mathrm{~m} / \mathrm{s}\), respectively. The compressor efficiency is \(\eta=0.85\). Calculate the mass flow rate of natural gas through the pipeline. Label state points on a \(T s\) diagram for compressor inlet and outlet. Evaluate the gas temperature and speed at the compressor outlet and the power required to drive the compressor.