Question

Natural gas as a mixture of 75% methane CH4 and 25% ethane C2H6 by moles is flowing to a compressor at 290 K and 100 KPa. The reversible adiabatic compressor brings the flow to 250 KPa. Find the exit temperature.

Answer 1

To find the exit temperature, use the adiabatic compression equation: T2 = T1 × (P2 / P1)^((y-1)/y). Plugging in the given values, T2 = 325 K.

Step-by-step explanation:

To find the exit temperature of the natural gas flowing to the compressor, we can use the adiabatic compression equation:

T2 = T1 × (P2 / P1)^((y-1)/y)

Where T1 is the initial temperature (290 K), P1 is the initial pressure (100 KPa), P2 is the final pressure (250 KPa), and y is the specific heat ratio.

For natural gas, y is typically around 1.3. Plugging in these values, we can calculate the exit temperature.

T2 = 290 K × (250 KPa / 100 KPa)^((1.3-1)/1.3)

T2 = 290 K × (2.5)^((0.3)/1.3)

T2 = 325 K