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What is the coefficient of performance of an ideal heat pump that has heat transfer from a cold temperature of $-25.0^{\circ} \mathrm{C}$ to a hot temperature of $40.0^{\circ} \mathrm{C}$ ?

$C O P_{\mathrm{hp}}=4.82$

Physics 101 Mechanics

Chapter 15

Thermodynamics

Thermal Properties of Matter

The First Law of Thermodynamics

The Second Law of Thermodynamics

Yanna B.

July 4, 2021

A heat engine has constant reservoir temperature of 9000 k and 4500 k what is the maximum efficiency of the engine

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in this question, we're supposed to find coefficient of heat performance. Seiko Peak. See which P s given by heat supplied, Divided by who have done. Now we are given only cold temperature and heart temperature. So let's force right this in terms of efficiency. Cute about it by efficiency Times Cube. So work done is efficiency times the heat supplied. So this is equal to one divided by efficiency. Now efficiency of Carnot engine, as we know, is given by one minus t c divided by th which is equal to one minus temperature off cold. Reasonable is 25 negative 25 degree Celsius. So converted into Kelvin is by adding to 70 thief on dhe Hot temperature is fortunately sense. Yes, so 14 plus 2 73 So let's do this. So this is equal to one minus to 48 divided by 13 13. So let's do this calculation. This gives me the efficiency as 0.21 So this is the efficiency. We have the maximum efficiency because this is Carlos efficiency. Now, as we know from this year, C o H p that is, they coefficient of performance off it. Heat engine is one divided by Aita, So this is equal to 01 divided by a point to let. So let's do that. This is equal to four point 762 So if you had instead used accuracy off three significant digits on written Aita as zero point 20766 So if you keep higher accuracy in this case on, use that value here instead of using 21 says you're a 0.20766 you will get the answer. Given we go. The question. So answer in the question answered. Even below the question is 4.82 And if you use this value, you will get that value, which is not far from this value. Thank you.

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