High School

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A Carnot air conditioner takes energy from the thermal energy of a room at 61°F and transfers it as heat to the outdoors at 98°F. For each joule of electric energy required to operate the air conditioner, how many joules are removed from the room?

Answer :

Answer:

14.07 units of joules is removed for each joules of electricity used

Explanation:

The heated room temperature [tex]T_{c}[/tex] = 61 °F

The outside temperature [tex]T_{h}[/tex] = 98 °F

For conversion from fahrenheit to kelvin we use the equation

(32°F − 32) × 5/9 + 273.15

[tex]T_{c}[/tex] = 289.26

[tex]T_{h}[/tex] = 309.82

For air conditioning,

COP = [tex]\frac{T_{c} }{T_{h} -T_{c} }[/tex]

COP = [tex]\frac{289.26 }{309.82 -289.26 }[/tex] = 14.07

This means that 14.07 units of joules is removed for each joules of electricity used

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