In a heat pump, heat from the outdoors at -2.42 degrees C is transferred to a room at 30.8 degrees C, with energy being supplied by an electric motor. How many joules of heat will be delivered to the room for each joule of electric energy consumed (ideally)

Respuesta :

Answer:

The value of heat transfer to the room = 9.145 J

Explanation:

Temperature of the room ([tex]T_{H}[/tex])  = 30.8 degree = 303.8 kelvin

Temperature of the Surrounding ([tex]T_{L}[/tex]) = - 2.42 degree = 270.58 kelvin

Electrical energy consumed (W) = 1 J

Heat transfer to the room is given by the formula [tex]\frac{Q_{H} }{W}[/tex] = [tex]\frac{T_{H} }{T_{H} - T_{L} }[/tex]

⇒ [tex]Q_{H}[/tex] = [tex]\frac{T_{H} }{T_{H} - T_{L} }[/tex] × W

Put all  the values in the above formula we get

⇒ [tex]Q_{H}[/tex] = [tex]\frac{303.8}{303.8 - 270.58}[/tex] × 1

[tex]Q_{H}[/tex] = 9.145 J

This is the value of heat transfer to the room.