Living cells "pump" singly ionized sodium ions, Na+, from the inside of the cell to the outside to maintain a membrane potential Δ V membrane = V in − V out = − 70 mV . It is called pumping because work must be done to move a positive ion from the negative inside of the cell to the positive outside, and it must go on continuously because sodium ions "leak" back through the cell wall by diffusion. How much work must be done to move one sodium ion from inside to the outside of the cell?

Air enters a gas turbine with two stages of compression and two stages of expansion at 100 kpa and 17°c. this system uses a regenerator as well as reheating and intercooling – the intercooler returns the air to the inlet temperature. the pressure ratio across each compressor is 4 ; 300 kj/kg of heat are added to the air in each combustion chamber; and the regenerator operates perfectly while increasing the temperature of the cold air by 20°c. determine the system’s thermal efficiency. assume isentropic operations for all compressor and the turbine stages and use constant specific heats at room temperature. (0.378)