Heat Pumps
(Published on 8. November 2024, 16:00 by Tobias Brixner)
Puzzle link: Play on SudokuPad.
Rules: Normal Sudoku rules apply.
A red-shaded rectangle represents a “heat pump”. For each of them, one connected arrow points from the heat pump to a neighboring cell containing the “hot temperature” Thot, and the other connected arrow points from a neighboring cell containing the “cold temperature” Tcold to the heat pump. For each heat pump separately, the temperatures fulfill Thot > Tcold.
Each heat pump contains its coefficient of performance (COP) in fractional notation with the numerator above and the denominator below the horizontal fraction line shown. The COP is calculated as the quotient of the hot temperature and the difference between the hot and the cold temperature, i.e., COP = Thot / (Thot - Tcold).
Each COP fraction must be reduced to lowest terms. A fraction is reduced to lowest terms by dividing the numerator and the denominator by their greatest common divisor. If the result is an integer number, 1 is entered in the denominator. For example, 8/6 must be entered as 4/3, and 8/4 as 2/1.
Your feedback, ratings and comments are highly appreciated. Have fun!
Background: A heat pump uses technical work W, extracts thermal energy from a reservoir at a low temperature and makes it available together with the energy input as useful heat Q for a system to be heated at a higher temperature. The coefficient of performance is defined as the ratio of the useful heat to the amount of energy used: COP = Q / |W|. For example, COP = 4 means that you get four times as much thermal energy Q for heating as you have to use in primary energy |W|. The COP should therefore be as high as possible. At a given outside temperature Tcold, COP increases as Thot decreases. For this reason, heating systems try to keep the flow temperature as low as possible in order to make optimum use of the fantastic “energy increase” provided by the additional heat from the environment. The formula given in the puzzle is the theoretical optimum according to the laws of thermodynamics. For real heat pumps, COPs are achieved which are in the order of magnitude of the values in the puzzle (COP = 3 ... 5 depending on the technical implementation and temperatures).
Example: You can play the 4x4 grid below yourself on SudokuPad.
Solution code: All digits of row 9 (from left to right) followed by column 9 (from top to bottom) without spaces.
Comments
on 10. November 2024, 13:44 by Firebird
It took me some time to grasp the rules. Then I had a lot of fun solving, thank you!
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Thank you so much! - TB
on 9. November 2024, 12:57 by marcmees
A million ways to take a wrong turn. Very nice. Thanks
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Glad you liked it! - TB
