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Freezing cold. Nastily I still have to do the laundry by hand. And to keep my hands from being frozen I have to add some hot water to the freezing tap water. Let's just suppose that I have the same amount of both. So the question is, should I add the hot water to the cold or add the cold to the hot, to make the final mixture as warm as possible? Which one will cause less heat loss? Any advice based on either life experience or physical analysis is appreciated. Thanks in advance.

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  • $\begingroup$ What do you think, and why? Where would you expect "excess heat" to dissipate to? "as warm as possible" is rather obviously solved with 100% hot and 0% cold water mix. $\endgroup$ Jan 23, 2015 at 16:49
  • $\begingroup$ ""... freezing tap water" How does this sound, when it falls down in the sink? $\endgroup$
    – Georg
    Jan 23, 2015 at 17:09
  • $\begingroup$ @Georg Well perhaps this description is not good, i'm sorry but i'm not a native speaker $\endgroup$
    – Vim
    Jan 23, 2015 at 17:14
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    $\begingroup$ @Vim Neither am I a native, but some fun is good always. $\endgroup$
    – Georg
    Jan 23, 2015 at 17:16
  • $\begingroup$ @CarlWitthoft I mean of course that I must mix them all. My question is about which first and which second so that the mixture is the warmer than when mixed otherwise $\endgroup$
    – Vim
    Jan 23, 2015 at 17:16

2 Answers 2

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If you are mixing both within a short time then it probably makes no noticeable difference.

If you are first tapping a half a bucket of hot water and then very slowly drip in the cold water then you will have rather hot mixture for a long time which will loose more heat to the environment than if if you do it the other way around.

I am pretty sure you can measure this quite easily if it takes half an hour to fill half a bucket, but for any normal speed (say using a regular water tap): Meh!

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  • $\begingroup$ Thank you but, since you say if I first tap half a bucket of hot water then drip in the cold I will have a hot mixture for a long time , why it will lose more heat to the environment than the other way round? Do you mean that if I do it the other way round it will lose even less heat and be even warmer? I'm a bit confused. $\endgroup$
    – Vim
    Jan 23, 2015 at 17:21
  • $\begingroup$ If you first tap hot water then you have a bucket of hot water (which I assume to be much hotter than the environment. Say T-ambient is 20°C and the hot water is 60°C (the minimum for hot water taps). That is a 40°C with the environment and it cooling down. If you start with cold water (flowing water, so at least 0°C and probably warmer) then it has a maximum of 20°C temperature with the environment. So it will warm up slower then the hot water (twice the delta temp) would have lost heat. $\endgroup$
    – Hennes
    Jan 23, 2015 at 17:32
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Adding the cold water to the hot will result in a warmer mix.

Heat radiates according to the Stefan–Boltzmann law, and the rate of heat loss is proportional to the forth power of the temperature. The quicker you can reduce the temperature of the hot water, the less heat will be lost.

If you add hot water to the cold, halfway through the process, you will have half the hot water left, still radiating quickly. If you add the cold water to the hot, the temperature of the hot water is reduced more quickly.

A variation of this problem is as follows: You drink your coffee after 5 minutes. To ensure you your coffee is as hot as possible, short you add cream immediately, or at the 5 minute mark?

If you add your cream immediately, heat loss from the cooler coffer will be less that if you add the cream after 5 minutes.

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    $\begingroup$ I'm unconvinced -- this argument seems to hinge on the relative insulating properties of the hot water container vs. the mixing container. $\endgroup$ Jan 23, 2015 at 18:07

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