Fuel cell system with exhaust gas mass flow determination

A fuel cell system has at least one fuel cell, an oxidant tube, a compressor, an exhaust gas tube, a turbine arranged in the exhaust gas tube, the turbine being coupled to the compressor, an anode flush tube connected to the exhaust gas tube and having an anode flush valve, and a control unit. The fuel cell system is characterized in that a temperature detection unit for detecting the temperature of the exhaust gas flowing into the turbine is arranged upstream at the turbine inlet or in front of the turbine inlet, and a pressure detection unit is coupled at least to the turbine inlet or to a component located upstream and is designed to detect the temperature of the exhaust gas flowing into the turbine. The pressure of the exhaust gas flowing into the turbine is detected, the control unit is configured to determine an instantaneous mass flow of the exhaust gas from the measured temperature of the exhaust gas, the pressure in front of the turbine and a predefined turbine characteristic curve, and the control u