An air conditioner operating at steady state maintains a dwelling at 70oF on a day when the outside temperature is 90oF. If the rate of heat transfer into the dwelling through the walls and roof is 30,000 Btu/h, might a net power input to the air conditioner compressor of 3 hp be sufficient? If yes, determine the coefficient of performance. If no, determine the minimum theoretical power input, in hp.

30000 btuh /3413 btuh/kw. = 8.8 kw

8.8 kw/.746 kw/hp = 11.8 hp if COP is 1

11.8/3 hp (COP coefficient of performance) = 3.99 COP

>>>So yes a 3.0 hp compressor with a nominal COP of 4 will handle the 30,000 btuh load.

3.2 to 4.5 is expected COP range for an air cooled heat pump or a/c unit.

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Cricetus Cricetus · Answer 2 · 2021-11-08T08:20:59+01:00

The power input of 3hP might be sufficient and the coefficient of performance will be "3.93".

According to the question,

In order to maintain the dwelling at 70°F with,

[tex]Q_{in} = 30000 \ Btu/h[/tex]

The COP,

→ [tex]\beta \leq \ \beta_{max}[/tex]

or,

→ [tex]\beta \leq \frac{T_c}{T_H-T_c}= \frac{530^{\circ} R}{(550-530)^{\circ}R}[/tex]

[tex]= 26.5[/tex]

or,

→ [tex]\frac{Q_{in}}{W_c} \leq 26.5[/tex]

→ [tex]W_c \geq \frac{3000 \ Btu/h}{26.5}\times \frac{1 \ hP}{2545 \ Btu/h}[/tex]

→ [tex]W_c \geq 0.445 \ hP[/tex] (minimum required power)

hence,

The corresponding COP will be:

→ [tex]\beta = \frac{Q_c}{W}[/tex]

[tex]= \frac{30000}{3\times 2545}[/tex]

[tex]= 3.93[/tex]

Thus the response above is correct.

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