The coefficient of performance K = H/P is a dimensionless quantit...

Question

The coefficient of performance K = H/P is a dimensionless quantity. Its value is independent of the units used for H and P, as long as the same units, such as watts, are used for both quantities. However, it is common practice to express H in Btu/h and P in watts. When these mixed units are used, the ratio H/P is called the energy efficiency ratio (EER). If a room air conditioner has K = 3.0, what is its EER?

Accepted Answer

Welcome back everybody. We are looking at the cooling efficiency of a refrigerator and we are given two formulas to describe that efficiency. The first one is the energy efficiency ratio, which is going to be the cooling capacity in british thermal units per hour divided by the power in watts. We are also going to describe it with a coefficient of performance, which is going to be the heat removal in watts, divided by the power in watts. And we are told that the coefficient of performance for this refrigerator is six and we need to find that energy efficiency Ratio. Well in order to work with these two formulas, I want to make sure that everything is in the same units here. So I'm actually going to convert our British thermal units per hour to watts here. So let's see in order to do that, we're going to take our British thermal units per hour and just multiply it by 0.293 to give us our cooling capacity in watts. And if you'll notice these two terms have the same units. So I'm going to just substitute in this part into our equation for our coefficient of performance, we have that. Kay is equal to .293 times our pulling capacity in british thermal units per hour divided by our power in watts. And if you'll notice this term right here is simply just our energy efficiency ratio. That means our coefficient of performance is equal to 0.293 times our e r. Now we can go and solve for e er I'm going to divide both sides by 0.293 here 0.293. This term is going to cancel out and we get that r e e R Is equivalent to our coefficient of performance divided by .293. Let's go ahead and plug in our number and solve our ER equal to six, divided by .293, giving us an energy efficiency ratio for this refrigerator of 20.5 corresponding to our answer choice of D. Thank you all so much for watching. Hope this video helped. We will see you all in the next one.

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