Chapter 21: Q. 21 (page 595)

An air conditioner removes $5.0 \times 10^{5} J / \min$ of heat from a house and exhausts $8.0 \times 10^{5} J / \min$ to the hot outdoors.
a. How much power does the air conditioner’s compressor require?
b. What is the air conditioner’s coefficient of performance?

Short Answer

Expert verified

(A) Air conditioner's require $5 kW,$

(B) Air conditioner coefficient of performance $\approx 1.7$

Step by step solution

Step :1 Introduction (part a)

(a) For a time of $t = 60 s$ we have $Q_{c} = 5 \cdot 10^{5} J and Q_{h} = 8 \cdot 10^{5} J$ . The corresponding powers are therefore

$\begin{aligned} P_{c} = \frac{Q_{c}}{t} = \frac{5 \cdot 10^{5}}{60} = 8333 W \\ P_{h} = \frac{Q_{h}}{t} = \frac{8 \cdot 10^{5}}{60} = 13333 W \end{aligned}$

$P_{c}$ is the power at which heat is removed and $P_{h}$ is the power at which heat is thrown into the environment . It will be sum of heat extracted and electrical power used up.

The power used up by the system can be calculated by

localid="1648567318756">P=Ph−Pc=13333−8333=5000W

Step :2 Explanation (part b)

(b) The coefficient performance can be calculated as

K $\frac{P o w e r e x t r a c e d}{p o w e r c o n s u m e d}$

$K = \frac{Q_{c}}{W} = \frac{P_{c} t}{P t} = \frac{P_{c}}{P}$

Numerically we will have

$K = \frac{8333}{5000} \approx 1.7$

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An air conditioner removes $5.0 \times 10^{5} J / \min$ of heat from a house and exhausts $8.0 \times 10^{5} J / \min$ to the hot outdoors.
a. How much power does the air conditioner’s compressor require?
b. What is the air conditioner’s coefficient of performance?

Short Answer

Step by step solution

Step :1 Introduction (part a)

Step :2 Explanation (part b)

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An air conditioner removes 5.0×105J/minof heat from a house and exhausts 8.0×105J/minto the hot outdoors.a. How much power does the air conditioner’s compressor require?b. What is the air conditioner’s coefficient of performance?

Short Answer

Step by step solution

Step :1 Introduction (part a)

Step :2 Explanation (part b)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Fields in Physics

Dynamics

Energy Physics

Solid State Physics

Electromagnetism

Mechanics and Materials

Study anywhere. Anytime. Across all devices.

An air conditioner removes $5.0 \times 10^{5} J / \min$ of heat from a house and exhausts $8.0 \times 10^{5} J / \min$ to the hot outdoors.
a. How much power does the air conditioner’s compressor require?
b. What is the air conditioner’s coefficient of performance?