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Question

In 1993, the U.S. government instituted a requirement that all room air conditioners sold in the United States must have an energy efficiency ratio (EER) of 10 or higher. The EER is defined as the ratio of the cooling capacity of the air conditioner, measured in British thermal units per hour, or Btu/h, to its electrical power requirement in watts. (a) Convert the EER of 10.0 to dimensionless form, using the conversion 1 Btu = 1 055 J. (b) What is the appropriate name for this dimensionless quantity? (c) In the 1970s, it was common to find room air conditioners with EERs of 5 or lower. State how the operating costs compare for 10 000-Btu/h airconditioners with EERs of 5.00 and 10.0. Assume each air conditioner operates for 1 500 h during the summer in a city where electricity costs $$17.0\phi$$ per kWh.


Solution

Conversion factor is given by $$1$$ Btu= $$1055$$ J
so $$EER=\dfrac{10 \times 1055}{3600}=2.93$$

By comparing the definitions of the COP and the EER, the appropriate name for this dimensionless quantity is the coefficient of performance of the air conditioner

The energy efficiency ratio is defined as:

$$\mathrm{EER}=\dfrac{\text { Cooling capacity }}{\text { Electric power }(P)}$$

Solve for $$P:$$

$$P=\dfrac{\text { Cooling capacity }}{\mathrm{EER}}$$

find the electric power of the first air conditioner using:

$$P =\dfrac{\text { Cooling capacity }}{(\mathrm{EER})_{1}}$$

$$=\dfrac{10000 \mathrm{Btu} / \mathrm{h}}{5 \dfrac{\mathrm{Btu} / \mathrm{h}}{\mathrm{W}}} $$

$$=(2000 \mathrm{W})\left(\dfrac{1 \mathrm{kW}}{1000 \mathrm{W}}\right) $$
$$=2 \mathrm{kW}$$

The operating cost of the first air conditioner is then:

$$\text { Operating costs } =(2 \mathrm{kW})(1500 \mathrm{h})(0.17 \$ / \mathrm{kWh}) $ $$

$$=510 \,$ $$

For second air conditioner:

$$P =\dfrac{\text { Cooling capacity }}{(\mathrm{EER})_{2}} $$

$$=\dfrac{10000 \mathrm{Btu} / \mathrm{h}}{10 \dfrac{\mathrm{Btu} / \mathrm{h}}{\mathrm{W}}} $$

$$=(1000 \mathrm{W})\left(\dfrac{1 \mathrm{kW}}{1000 \mathrm{W}}\right) $$

$$=1 \mathrm{kW}$$

The operating cost of the first air conditioner is then:
$$\text { Operating costs } =(1 \mathrm{kW})(1500 \mathrm{h})(0.17 \$ / \mathrm{kWh}) $$
$$=255 \,$ $$

Physics

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