A power cycle operating between hot and cold reservoirs at 500 K and 300 K, respectively, receives 1000 kJ by heat transfer from the hot reservoir. The magnitude of the energy discharged by heat transfer to the cold reservoir must satisfy

The value is

Explanation:

From the question we are told that  

   The temperature of  hot is  

   The temperature of cold is  

   The energy received is  

Generally the maximum thermal  efficiency of the engine is mathematically represented as

=>

=>

Generally the thermal  efficiency of the engine is  

Here   is the heat energy rejected

Generally the thermal efficiency must be less than or equal to the maximum thermal  efficiency

So

=>    

the change in inequality sign is because  which was dividing started multiplying

=>    

=>  

=>  

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