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I would like to find out how long it would take to completely turn 50 litres of water to steam. Let's assume power of 2500 W and the water is already at boil. I am not very scientific so please forgive any omissions. Thanks

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What actually happens in real life depends on a lot of things. Factors like the shape of the pot can make a big difference to how much of that 2500 W actually goes into vaporizing the water and how much of it is lost to the surroundings. If we assume that all 2500 W is going into the water, it makes things a lot simpler. If the water is already at the boiling point, then all we have to do is calculate the total amount of energy needed to vaporize all the water:

The enthalpy of vaporization of water is 40.65 $\mathrm{kJ/mol}$, which means 40.65 kJ of heat needs to be added to turn one mole of liquid water to steam. 50 L of water is 2775 moles: $$\mathrm{\frac{(50\ L)\left(1000\frac{g}{L}\right)}{\left(18.02\frac{g}{mol}\right)}=2775\ mol}$$

So the total heat we need is: $$\mathrm{(2775\ mol)\left(40.65\frac{kJ}{mol}\right)=112.8\ MJ}$$

1 watt is one joule per second, so for a 2500 W heat source: $$\mathrm{\frac{112.8\ MJ}{2500\ J/s}=45\ ks}$$ Or, approximately 12.5 hours. In real life, it may be significantly longer for various reasons, but this is the fastest it could go.

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  • $\begingroup$ Thank you. I suspected around 12 hours, but never considered the other factors you mention. Your explanation is much appreciated $\endgroup$
    – David
    Dec 24 '14 at 4:34

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