1000 kg/hr of water at 1 bar is fed to a pump, where the pressure of the water is increased to 20 bar in an adiabatic manner. The high-pressure water is fed to a isobaric furnace. In the furnace, natural gas (primarily CH4) is burnt and most of the heat generated is transferred to the water, which leads to steam at 300 C and 20 bar being produced. The steam is then fed to an adiabatic turbine, where it is expanded and then exits as saturated vapor at 1 bar. This exhaust steam is sent to an isobaric condenser to cool and produce saturated liquid. This saturated liquid is the feed to the pump. During the pumping, the temperature of the water increases slightly to 110 C. The complete steady cyclic process is as shown. The work generated in the turbine is in the form of electricity and the pump operates by an electric motor that consumes electricity. Thus, the cyclic process produces net electricity.
(i). Calculate the work produced by the turbine, the heat that has to be transferred to the water in the furnace from natural gas, the heat removed in the condenser, and the shaft work required by the pump. Clearly state assumptions for each unit.
(ii). If the furnace efficiency is 81%, i.e. 81% of the heat generated by combusting methane is transferred, calculate the amount (kg/hr) of natural gas burnt in the furnace using the results from above part. The heating value of natural gas can be assumed to be 55.6 MJ per kg CH4 burnt.