Thermodynamics, Statistical Physics, and Quantum Mechanics

94

So

where we used for an estimate the fact thatTdoes not changesignificantly

and Then the time for the tea to cool from the

initial temperature to thefinal temperature is given by

4.10 Heat Loss (Moscow Phys-Tech)

Let min be the time the heateris operating. The energy added to
the water and bowl will heat the water aswell as theenvironment. We
will assumethat theheatloss to thesurroundings is proportional to the
elapsed time and that thechangingtemperaturedifference between
the water and room temperature Duringthis phase, we may
write

The heatloss isactually a time integral ofsomeproportionalityconstant
times the temperaturedifference as the water heats up.However, only
varies by out of an average so we willignore the variation. The
heatlossduring thesecond phase is given by

SOLUTIONS