A heat pump is a heating system installed on some newer houses. It works by pumping heat from outside to inside. The efficiency of the heat pump is given by QH W where W is the work done by an electric motor. The maximum theoretical efficiency of a heat pump is TH NHP mar TH – TC 1. If the temperature outside is 44°F and the temperature inside is 65°F (these are the current temperatures outside and inside my apartment as I write this problem) what is the maximum possible efficiency of a heat pump. (Hint: You need to convert both temperatures to Kelvin first. Google can do this conversion for you.) 2. Calculate the volume of your house by multiplying the square footage by the ceiling height. For example, my apartment is 1025ft² and has a 8ft ceiling. (If you don't know your square footage, you can use mine.) Convert your answer into m³. 3. The density of air is 1.2 . What is the mass of air in your house (neglect the furniture etc. in your house). 4. The specific heat of air is 1.0 k. How much heat energy is need to heat the air by 10K? Hint: use Q = mcAT. kgK· 5. How many Joules of electricity would this take if I had a perfect heat pump. 6. The answer to question 5 should be less than the answer to question 4. This sounds too good to be true, how is it possible? 7. If we pay $0.15/kWhr, how much would it cost to increase the temperature in my house by 10K?
A heat pump is a heating system installed on some newer houses. It works by pumping heat from outside to inside. The efficiency of the heat pump is given by QH W where W is the work done by an electric motor. The maximum theoretical efficiency of a heat pump is TH NHP mar TH – TC 1. If the temperature outside is 44°F and the temperature inside is 65°F (these are the current temperatures outside and inside my apartment as I write this problem) what is the maximum possible efficiency of a heat pump. (Hint: You need to convert both temperatures to Kelvin first. Google can do this conversion for you.) 2. Calculate the volume of your house by multiplying the square footage by the ceiling height. For example, my apartment is 1025ft² and has a 8ft ceiling. (If you don't know your square footage, you can use mine.) Convert your answer into m³. 3. The density of air is 1.2 . What is the mass of air in your house (neglect the furniture etc. in your house). 4. The specific heat of air is 1.0 k. How much heat energy is need to heat the air by 10K? Hint: use Q = mcAT. kgK· 5. How many Joules of electricity would this take if I had a perfect heat pump. 6. The answer to question 5 should be less than the answer to question 4. This sounds too good to be true, how is it possible? 7. If we pay $0.15/kWhr, how much would it cost to increase the temperature in my house by 10K?
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Use 1025ft2 and 8ft
![A heat pump is a heating system installed on some newer houses. It works by pumping heat from outside to inside. The efficiency of the heat pump is given by:
\[
\eta = \frac{Q_H}{W}
\]
where \( W \) is the work done by an electric motor. The maximum theoretical efficiency of a heat pump is:
\[
\eta_{HP \ max} = \frac{T_H}{T_H - T_C}
\]
1. If the temperature outside is 44°F and the temperature inside is 65°F (these are the current temperatures outside and inside my apartment as I write this problem) what is the maximum possible efficiency of a heat pump. (Hint: You need to convert both temperatures to Kelvin first. Google can do this conversion for you.)
2. Calculate the volume of your house by multiplying the square footage by the ceiling height. For example, my apartment is 1025ft² and has a 8ft ceiling. (If you don’t know your square footage, you can use mine.) Convert your answer into m³.
3. The density of air is \( 1.2 \, \text{kg/m}^3 \). What is the mass of air in your house (neglect the furniture etc. in your house).
4. The specific heat of air is \( 1.0 \, \text{kJ/kgK} \). How much heat energy is needed to heat the air by 10K? Hint: use \( Q = mc\Delta T \).
5. How many Joules of electricity would this take if I had a perfect heat pump.
6. The answer to question 5 should be less than the answer to question 4. This sounds too good to be true, how is it possible?
7. If we pay $0.15/kWh, how much would it cost to increase the temperature in my house by 10K?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc11f26fd-cef8-49ce-a518-26ea804f3de8%2F992611b4-4ee1-476d-9ff9-42f24d80807c%2Fg9ml8b_processed.png&w=3840&q=75)
Transcribed Image Text:A heat pump is a heating system installed on some newer houses. It works by pumping heat from outside to inside. The efficiency of the heat pump is given by:
\[
\eta = \frac{Q_H}{W}
\]
where \( W \) is the work done by an electric motor. The maximum theoretical efficiency of a heat pump is:
\[
\eta_{HP \ max} = \frac{T_H}{T_H - T_C}
\]
1. If the temperature outside is 44°F and the temperature inside is 65°F (these are the current temperatures outside and inside my apartment as I write this problem) what is the maximum possible efficiency of a heat pump. (Hint: You need to convert both temperatures to Kelvin first. Google can do this conversion for you.)
2. Calculate the volume of your house by multiplying the square footage by the ceiling height. For example, my apartment is 1025ft² and has a 8ft ceiling. (If you don’t know your square footage, you can use mine.) Convert your answer into m³.
3. The density of air is \( 1.2 \, \text{kg/m}^3 \). What is the mass of air in your house (neglect the furniture etc. in your house).
4. The specific heat of air is \( 1.0 \, \text{kJ/kgK} \). How much heat energy is needed to heat the air by 10K? Hint: use \( Q = mc\Delta T \).
5. How many Joules of electricity would this take if I had a perfect heat pump.
6. The answer to question 5 should be less than the answer to question 4. This sounds too good to be true, how is it possible?
7. If we pay $0.15/kWh, how much would it cost to increase the temperature in my house by 10K?
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