Problem # p008

Carnot Efficiency, Heatpump

A manufacturer claims that his/her heat pump extracts heat from the environment at 0°C and keeps the inside of a house at 25°C and that the heatpump has a coefficient of performance (=ratio of benefits to costs) of 13.

Use the following symbols in your work :
1)     QH = heat supplied to the house by heat pump
2)     QC = heat extracted from the cold environment by the heat pump
3)     W = work needed to run the heat pump

  1. Give the equation which relates above 3 quantities to each other.

  2. Which of the above 3 quantities would be identified with the benefit ?

  3. Which of the above 3 quantities would be identified with the costs ?

  4. Which is the best value for the ratio QC/QH for the given temperatures and what would the coefficient of performance (benefit divided by costs) be for this case ?

  5. Is the manufacturer's claim of 13 for his/her coefficient of performance reasonable ? State in a short sentence the reason for your conclusion.