Air conditioners sold in the United States are given a seasonal energy-efficiency ratio (SEER) rating that consumers can use to compare different models. A SEER rating is the ratio of heat pumped to energy input, similar to a COP but using English units, so a higher SEER rating means a more efficient model. You can determine the COP of an air conditioner by dividing the SEER rating by 3.4.

Question

Air conditioners sold in the United States are given a seasonal energy-efficiency ratio (SEER) rating that consumers can use to compare different models. A SEER rating is the ratio of heat pumped to energy input, similar to a COP but using English units, so a higher SEER rating means a more efficient model. You can determine the COP of an air conditioner by dividing the SEER rating by 3.4.

For inside temperature 26 ∘C and outside temperature 33 ∘C when you'd be using air conditioning, estimate the theoretical maximum SEER rating of an air conditioner. (New air conditioners must have a SEER rating that exceeds 13, quite a bit less than the theoretical maximum, but there are practical issues that reduce efficiency.)

Answer 1

To estimate the theoretical maximum SEER rating of an air conditioner, we need to calculate the COP (Coefficient of Performance) first and then convert it to SEER rating.

The COP of an air conditioner can be calculated using the formula:

COP = (Amount of cooling produced) / (Amount of energy input)

In this case, the amount of cooling produced is the difference between the inside and outside temperatures, which is (33 - 26) = 7°C.

So, the COP of the air conditioner would be:

COP = 7°C / Energy input

Now, we need to convert the COP to SEER rating. The conversion is done by dividing the SEER rating by 3.4:

SEER = COP / 3.4

Let's calculate the theoretical maximum SEER rating using the given temperatures:

COP = 7°C / Energy input

SEER = COP / 3.4

Since we don't have the specific value for the energy input, we cannot calculate the exact SEER rating. However, this formula allows us to compare different models of air conditioners based on their energy efficiency.

It's important to note that the theoretical maximum SEER rating is used as a benchmark and does not necessarily reflect the efficiency of all available air conditioner models in the market. Practical issues and limitations can reduce the actual efficiency rating of air conditioners.

Answer 2

To estimate the theoretical maximum SEER rating of an air conditioner, we need to calculate the Coefficient of Performance (COP) first. The formula to calculate COP is:

COP = Heat Pumped / Energy Input

Given that the SEER rating is defined as the ratio of heat pumped to energy input, we know that:

SEER = Heat Pumped / Energy Input

Rearranging the equation, we can solve for Heat Pumped:

Heat Pumped = SEER * Energy Input

Now, we can substitute the values given:

Inside Temperature = 26 °C
Outside Temperature = 33 °C

The heat pumped by the air conditioner is equal to the heat transferred from the indoors to the outdoors. The maximum heat that can be transferred is obtained when the indoor and outdoor temperatures are equal. Therefore, we calculate the temperature difference:

Temperature Difference = Outside Temperature - Inside Temperature
= 33 °C - 26 °C
= 7 °C

Assuming an ideal air conditioner, we know that the heat pumped is proportional to the temperature difference. Hence, Heat Pumped = Temperature Difference.

Now we have:

Heat Pumped = 7 °C
Energy Input = 1

Substituting these values, we can calculate the SEER rating:

SEER = Heat Pumped / Energy Input
= 7 °C / 1
= 7

Finally, to estimate the theoretical maximum SEER rating, we divide the SEER rating by 3.4:

Maximum Theoretical SEER = SEER / 3.4
= 7 / 3.4
≈ 2.059

Therefore, the theoretical maximum SEER rating of an air conditioner under the given conditions is approximately 2.059.

Answer 3

eff = Q/W = T2/(T1-T2)

T2 = 26 + 273
T1-T2 = 33-26 = 7
eff = 299/7 = 42.7