A 0.6 m diameter gas pipeline is being used for the long-distance transport of natural gas. Just past a pumping station, the gas is found to be at a temperature of 25^◦C and a pressure of 3.0 MPa. The mass flow rate is 125 kg/s, and the gas flow is adiabatic. Forty miles down the pipeline is another pumping station. At this point the pressure is found to be 2.0 MPa. At the pumping station the gas is first adiabatically compressed to a pressure of 3.0 MPa and then isobarically (i.e., at constant pressure) cooled to 25^◦C.

a. Find the temperature and velocity of the gas just before it enters the pumping station. 

b. Find the rate at which the gas compressor in the pumping station does work on the gas, the temperature of the gas leaving the compressor, and the heat load on the gas cooler. You may assume that the compressor exhaust is also a 0.6-m pipe.

Natural gas can be assumed to be pure methane [molecular weight = 16, C^∗_P = 36.8 J/(mol K)], and an ideal gas at the conditions being considered here. Note that the mass flow rate M is ρvA, where ρ is the mass density of the gas, v is the average gas velocity, and A is the area of the pipe.