Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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Problem G. 654. (December 2018)

G. 654. The height of the thermal water of temperature $\displaystyle 30\;{}^\circ$C in a spa pool of base $\displaystyle 12~\mathrm{m}\times 20~\mathrm{m}$ is 75 cm. The pool was then filled with $\displaystyle 50\;{}^\circ$C water up to the height of 1 m. Due to heat loss the temperature of the mixture is $\displaystyle 2\;{}^\circ$C less than it would be without the loss. What amount of heat was lost during mixing the water?

(3 pont)

Deadline expired on January 10, 2019.

Sorry, the solution is available only in Hungarian. Google translation

Megoldás. A medencében összesen $\displaystyle 240~\rm m^3$ termálvíz van, amelynek tömege 240\,000 kg. Ha ennyi víz $\displaystyle 2\,^\circ$C-kal lehűl, a leadott hő (tehát a hőveszteség)

$\displaystyle Q=\left(4{,}2\,\frac{\rm kJ}{\rm kg\,^\circ \rm C}\right)\cdot (2{,}4\cdot 10^5~{\rm kg})\cdot(2\,^\circ\rm C)\approx 2\cdot10^9~{\rm J}=2~\rm GJ.$