Each second, the fuel burning in an electric power plantproduces 1000 MJ of heat

Question

Each second, the fuel burning in an electric power plantproduces 1000 MJ of heat energy at a temperature of 527ºC andreleases waste heat into a cooling pond at 27ºC.
(a)What is the maximum (Carnot) efficiency of the power plant?
(b)If the plant operates at half the maximum efficiency, what isthe power output of the plant?
(c)How much heat is rejected each second to the cooling pond eachsecond? Each second, the fuel burning in an electric power plantproduces 1000 MJ of heat energy at a temperature of 527ºC andreleases waste heat into a cooling pond at 27ºC.
(a)What is the maximum (Carnot) efficiency of the power plant?
(b)If the plant operates at half the maximum efficiency, what isthe power output of the plant?
(c)How much heat is rejected each second to the cooling pond eachsecond?

Explanation / Answer

   Temperature of hot reservoir(source)  T1    =   5270C                                                                          =   527+ 273                                                                      =   800   K    Temperature ofsink   T2   =   270C                                           =   27+ 273                                           =   300   K    Inputpower   Pin   =   1000   MJ/ s   =   1000 MW    a.   Carnotefficiency          =   1   -   (T2/ T1)                                                 =   1   -   300/ 800                                                 =   0.625                                                 =   62.5%    b.   Efficiency at half themaximumvalue   '   =   / 2                                                                         =   0.625/ 2                                                                         =   0.3125          Also      =   Outputpower / input power                   0.3125   =   Pout/ Pin                   Pout   =   0.3125* 1000 MW                            =   312.5   MW    c.   Heat wasted persecond   Prej   =   Pin   -   Pout          Prej   =   1000   -   312.5                  =   678.50   MW                   =   678.5   MJ/ s          Prej   =   1000   -   312.5                  =   678.50   MW                   =   678.5   MJ/ s

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