Red Stack: Heating/Cooling

Next, we will break down the energy required by an American for heating purposes.

Showers

Since most Americans take showers, we will be disregarding anything dealing with baths.

We assume 1, 10 minute shower a day from a 3 GPM shower head,  120 F bath temp and 70 F inlet temp.

The specific heat of water is also 4.18 J/gK

Using Q=m*Cp*deltaT we get Q= 23.7 MJ or 6.58 kWh/person/day


Appliances 

The following usage times can vary substantially from one person to the next.  The values used were estimates for an average college student.  Families would use each appliance for a longer period of time. (All times per day)

Microwave- 5 min
Oven- 20 min
Washing Machine- 5 min
Dryer- 5 min
Dishwasher- 10 min
Refrigerator- 24 hours
Freezer- 24 hours

The power consumption values used were from the McKay book.  Although Britain has a higher voltage supply than the US, the kWh values will still be the same.

The total energy used from appliances comes to 4.7 kWh/person/day

HVAC- Heating

The average American house is 2,700 sq. ft. (National Homebuilders Association), and assuming an 8 ft ceiling contains 21,600 ft^3 of air.  Taking into account an air exchange factor of 1/2 hr, and a air density of 0.08 lb/ft^3, 83,136 lbs of air must be heated per day.

Taking the specific heat of air to be 0.241 BTU/lb*F, and assuming an outside temp of 30 F and inside temp of 65 F.  We again use Q=m*Cp*deltaT

Q= 83138*0.241*(65-30) = 701206 BTU = 205 kWh/day

Assuming a family of four in the house: 205/4 people = 50 kWh/person/day


HVAC-Cooling

The efficiency for an air conditioner is measured using the seasonal energy efficiency ratio (SEER), which equal BTU of output/ wH of input.

Assuming an outside temp of 85 F and inside temp of 70 F, and also using the same house dimensions and lb of air cooled as above, we can find the required BTU per day.

Q = 83136*0.241*(85-70) = 300536.64 BTU required.

Looking on Trane air conditioner website, an average model has a SEER of 13, which we can use to find the kWh required per day.

13 = 300536.64/ kWh required;  23.1 kWh required/ 4 people = 5.8 kWh/person/day


Conclusion

The heating value calculated is much higher than the value found in McKay.  This could be due to the fact that American households are bigger, on average, than those in Britain.  Also, McKay is talking about using space heaters in specific rooms, while Americans typically heat the whole house to the desired value.

Also, it can be seen that the energy required to cool air is calculated to be a lot less than what is required to heat the air.  This seemed counter-intuitive to the group, but after further thought the difference can be traced back to the air temperature assumptions.  The temperatures assumed for cooling are a lot closer to one another than those assumed for heating