### Problem 2**(II)** An ideal heat pump is used to maintain the inside temperature of a house at \( T_{in} = 22°C \) when the outside temperature is \( T_{out} \). Assume the heat pump does work at a rate of 1700 W. Also assume that the house loses heat via conduction through its walls and other surfaces at a rate given by \( (650 \, W/°C) \cdot (T_{in} - T_{out}) \).(a) For what outside temperature would the heat pump have to operate at all times in order to maintain the house at an inside temperature of 22°C?(b) If the outside temperature is less than you just calculated, what happens?(c) If the outside temperature is 8°C, what percentage of the time does the heat pump have to operate in order to maintain the house at an inside temperature of 22°C?**Note for instructors**: This problem requires students to understand the relationship between temperature differences, heat loss, and work provided by a heat pump. The problem also involves calculating operating conditions for different exterior temperatures and interpreting the results. ### Solution Outline1. **Identify given data and equations:** - Inside temperature, \( T_{in} = 22°C \) - Heat pump work rate, \( P = 1700W \) - Heat loss: \( Q_{loss} = (650 \, W/°C) \cdot (T_{in} - T_{out}) \)2. **Set the equations:** - For the heat pump to operate all the time: \( P = Q_{loss} \) - Solve for \( T_{out} \)3. **Analyzing temperature impacts:** - What happens when \( T_{out} \) is lower - Calculating operating percentage based on given \( T_{out} \)This problem offers insights into thermodynamics and energy efficiency, common topics in physics and engineering curricula.

Given data Inside temperature of house = Tin = 22 °Cheat pump does a work rate = 1700 WThe heat loss…

- (II) An ideal heat pump is used to maintain the inside temperature of a house at Tin = 22°C when the outside temperature is Tout Assume the heat pump does work at a rate of 1700 W. Also assume that the house loses heat via conduction through its walls and other surfaces at a rate given by (650 W/C°) (Tin - Tout). (a) For what outside temperature would the heat pump have to operate at all times in order to maintain the house at an inside temperature of 22°C? (b) If the outside temperature is less than you just calculated, what happens? (c) If the outside temperature is 8°C, what percentage of the time does the heat pump have to operate in order to maintain the house at an inside temperature of 22°C?

- (II) An ideal heat pump is used to maintain the inside temperature of a house at Tin = 22°C when the outside temperature is Tout Assume the heat pump does work at a rate of 1700 W. Also assume that the house loses heat via conduction through its walls and other surfaces at a rate given by (650 W/C°) (Tin - Tout). (a) For what outside temperature would the heat pump have to operate at all times in order to maintain the house at an inside temperature of 22°C? (b) If the outside temperature is less than you just calculated, what happens? (c) If the outside temperature is 8°C, what percentage of the time does the heat pump have to operate in order to maintain the house at an inside temperature of 22°C?

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

### Problem 2

**(II)** An ideal heat pump is used to maintain the inside temperature of a house at \( T_{in} = 22°C \) when the outside temperature is \( T_{out} \). Assume the heat pump does work at a rate of 1700 W. Also assume that the house loses heat via conduction through its walls and other surfaces at a rate given by \( (650 \, W/°C) \cdot (T_{in} - T_{out}) \).

(a) For what outside temperature would the heat pump have to operate at all times in order to maintain the house at an inside temperature of 22°C?

(b) If the outside temperature is less than you just calculated, what happens?

(c) If the outside temperature is 8°C, what percentage of the time does the heat pump have to operate in order to maintain the house at an inside temperature of 22°C?

**Note for instructors**: This problem requires students to understand the relationship between temperature differences, heat loss, and work provided by a heat pump. The problem also involves calculating operating conditions for different exterior temperatures and interpreting the results.

### Solution Outline

1. **Identify given data and equations:**
- Inside temperature, \( T_{in} = 22°C \)
- Heat pump work rate, \( P = 1700W \)
- Heat loss: \( Q_{loss} = (650 \, W/°C) \cdot (T_{in} - T_{out}) \)

2. **Set the equations:**
- For the heat pump to operate all the time: \( P = Q_{loss} \)
- Solve for \( T_{out} \)

3. **Analyzing temperature impacts:**
- What happens when \( T_{out} \) is lower
- Calculating operating percentage based on given \( T_{out} \)

This problem offers insights into thermodynamics and energy efficiency, common topics in physics and engineering curricula.

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