channel for cooling the mixer after at least partly cooling the mixer the cooling gas 33 is fed into the dilution gas inlet 19 and admixed to the hot gas as dilution gas 32 in the mixer 12 compressed gas 8 is also fed into the fourth cooling channel 18 as cooling gas 33 at a downstream end relative to the hot gas flow direction and flows in counter flow to the main flow direction of the hot gas flow in the second combustion chamber 14 after passing through the fourth cooling channel 18 the cooling gas 33 enters the third cooling channel 17 at a downstream end relative to the hot gas flow direction and flows in counter flow to the main flow direction of the hot gas flow in the second burner 13 after cooling the second combustion chamber wall 27 and the second burner wall 26 the cooling gas 33 is fed to the second burner 13 the cooling gas 33 can for example be fed to the second burner 13 as cooling gas e g as film cooling gas or diffusion cooling part of the cooling gas 33 can already be fed to the hot gas 9 in the second combustion chamber 14 during cooling of the second combustion chamber wall 27 not shown a first fuel 28 can be introduced into the first burner 10 via a first fuel injection mixed with compressed gas 8 which is compressed in the compressor 3 and burned in the first combustion chamber 11 dilution gas 32 is admixed in the subsequent mixer 12 a second fuel 29 can be introduced into the second burner 13 via a second fuel injector 51 mixed with hot gas leaving the mixer 12 and.