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Fundamentals Of Physics
Found in: Page 606

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Short Answer

An air conditioner operating between 93°Fand 70°F is rated at 4000Btu/h cooling capacity. Its coefficient of performance is 27% of that of a Carnot refrigerator operating between the same two temperatures. What horsepower is required of the air conditioner motor?

The power of the air conditioner motor is |0.25hp .

See the step by step solution

Step by Step Solution

Step 1: The given data

Temperatures at which the air conditioner operates are TL=70°F=294 K and TH=93°F=307 K .

The cooling capacity of the air conditioner, QLt=4000Btu/h

Coefficient of performance of Carnot refrigerator, K=0.27Kc

Step 2: Understanding the concept of the Carnot refrigerator

The coefficient of performance of the Carnot refrigerator is given. Using this, we can find the coefficient of performance of the air conditioner. Once we get that, using the relation between work done, coefficient of performance and heat absorbed we find the horsepower of the motor.

Formulae:

Coefficient of performance of Carnot refrigerator,

Kc=TLTH-TL (1)

The work done per cycle of the Carnot engine,

W=QK (2)

Step 3: Calculation of power of air conditioner

From the given value of the coefficient of performance and using equation (1), we can get the coefficient of performance of the air conditioner as given:

K=0.27×TLTH-TL =0.27×294 K307 K - 294 K =0.27×23 =6.21

Dividing t into both sides of equation (2), we can get the power of the air conditioner as given:

Wt=QL/tK =40000Btu/h6.21 =643 Btu/h =643 Btu/h×0.0003929hp1 Btu/h =0.25hp

Hence, the value of the required power is 0.25 hp

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