Heat pump and temperature in the house

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SUMMARY

The discussion focuses on calculating the time required for a heat pump with a Coefficient of Performance (COP) of 2.5 to raise the temperature of a house from 3°C to 22°C. The heat pump consumes 8 kW of electrical power and the house loses heat at a rate of 40,000 kJ/h. Given the total mass of the house's contents is 2000 kg with specific heat capacities of Cv=0.728 kJ/(kg·K) and Cp=1.005 kJ/(kg·K), the effective heat added by the pump must be determined to find the duration for the temperature increase.

PREREQUISITES
  • Understanding of heat transfer principles
  • Knowledge of Coefficient of Performance (COP) in heat pumps
  • Familiarity with specific heat capacities (Cp and Cv)
  • Basic thermodynamic equations and calculations
NEXT STEPS
  • Calculate the effective heat output of the heat pump using its COP
  • Determine the net heat gain by subtracting heat loss from heat added
  • Use the specific heat capacity to calculate the temperature change over time
  • Explore advanced heat pump efficiency metrics and their impact on performance
USEFUL FOR

Students in thermodynamics, HVAC engineers, and anyone involved in energy efficiency and heating system design will benefit from this discussion.

Kuddus
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Homework Statement


A heat pump with COP of 2.5 is used to heat a house. When operating, the heat pump cosumes 8kW of electrical power. If the house is losing heat to the outside at an average rate of 40000 kj/h and the temperature of the house is 3 degree celsius when the heat pump is turned on, determine how long it will take for the temperature in the house to rise to 22 degree celsius. Assume the house is well sealead ( i.e. no airl leaks) and take the entire mass within the house (air, door , furniture , etc) tobe equal to 2000kg of air for which Cv=0.728 kJ/(kg.K) and Cp= 1.005 kJ/(kg.K)


Homework Equations


Cp/Cv=gamma



The Attempt at a Solution

 
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I would start by figuring out at what rate the heat pump adds heat to the house.
 

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