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A heat pump with a 2 kW motor is used to heat a building at 30 deg C. The building loses heat at a rate of 0.5 kW per degree difference to the colder ambient at T amb. The heat pump has a coefficient of performance that is 50 % of a carnot heat pump. What is the maximum ambient temperature for which the heat pump is sufficient?

Respuesta :

Answer:

T=5.3° C

Explanation:

Given that

Power input to the pump = 2 KW

Building loses heat rate = 0.5 KW/C

So rate of heat transfer = 0.5(273+30-T)

rate of heat transfer = 0.5(303-T)

T=Ambient temperature

Building temperature = 30° C

We know that ,heat pump is used to heat the building.

COP of pump = 0.5 COP of Carnot heat pump

[tex]COP\ of\ Carnot\ heat\ pump=\dfrac{273+30}{303-T}[/tex]

[tex]COP\ of\ Carnot\ heat\ pump=\dfrac{303}{303-T}[/tex]

[tex]COP\ of\ pump=\dfrac{303-T}{Power}[/tex]    

[tex]COP\ of\ pump=0.5\times \dfrac{303-T}{2}[/tex]     -----1

And also

[tex]COP\ of\ pump=\dfrac{1}{2}\times \dfrac{303}{303-T}[/tex]   ----2

So from now equation 1 and 2

[tex]\dfrac{303-T}{4}=\dfrac{1}{2}\times \dfrac{303}{303-T}[/tex]

So T= 278.38 K=5.3° C

T=5.3° C

Ambient temperature =5.3° C.

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