A heat pump is under consideration for heating a research station located on an Antarctica ice shelf. The interior of the station is to be kept at 158C. Determine the maximum theoretical rate of heating provided by a heat pump, in kW per kW of power input, in each of two cases: The role of the cold reservoir is played by (a) the atmosphere at 2208C, (b) ocean water at 58C

a

The heat provided is  

b

The heat provided is  

Explanation:

From the  question we are told that

        The temperature of interior is

The coefficient of performance of the heater is  

Where is the temperature of the cold reservoir with a value  

          So    

The coefficient of performance is also represented mathematically as

Let assume the workdone is  = 1 N m

 The coefficient of performance of the heater is  

Where is the temperature of the cold reservoir with a value  

          So    

The coefficient of performance is also represented mathematically as

Let assume the workdone is  = 1 N m

a chemical reaction

explanation: