1
$\begingroup$

My question is the following: I have two pots. Pot A and pot B. I fill both of them with 1l (litre) of water. Now I add a table spoon of salt into pot A. Which water is going to start boiling first?

I was researching this question and came across two posts on this website:

Salt and boiling speed

Does salt affect the boiling time of water?

The first one states the following:

Adding salt increases the boiling point, so you need to get the salt solution hotter to make it boil. However for saturated salt solution the specific heat falls by about 22% while the boiling point only goes up by 8%, so the salt solution still boils faster even taking into account the elevated boiling point. However for saturated salt solution the specific heat falls by about 22% while the boiling point only goes up by 8%, so the salt solution still boils faster even taking into account the elevated boiling point.

The second one states the following:

It depends on how much salt you add.

So is it now dependent on the amount of salt or not?

After looking on google you can find answers on quora for example that say adding salt decreases the time until the water starts boiling and also answers that state the opposite.

What is now the case? Is it even possible to give a simple answer?

On quora I found an answer stating the following thing:

BUT, if you have the same amount of water in two pots and you add salt to one and not the other, the one without the salt will boil quicker.

What am I missing?

$\endgroup$
2
  • 2
    $\begingroup$ It takes quite a bit more than a tablespoon of salt to saturate 1 liter of water, so your data are inconsistent. In addition, it's easily possible to calculate the ratio of times that it takes to boil each solution, but the mass of the salt increases the mass that must be heated, so that information is also needed. $\endgroup$ Oct 6, 2023 at 18:10
  • $\begingroup$ @DavidWhite True but nevertheless many other websites don't even mention saturation. They just state adding salt into water. You mentioned that additional information is needed. Does it mean that it is dependent on the amount of salt added? $\endgroup$ Oct 6, 2023 at 18:33

1 Answer 1

1
$\begingroup$

The following variables apply to this problem:

$Q$ - the amount of heat transferred into each liter of water

$m_{water}$ - the mass of water in each container

$m_{salt}$ - the mass of salt in each container

$C_p$ - the specific heat of the given mixture

$\Delta T$ - the temperature change of each liter of water

$t$ - time

For these variables, the following heat equation applies:

$\frac{Q}{t} = \frac{(m_{water}+m_{salt})C_p \Delta T}{t}$

This equation can be solved for time required to reach the boiling point, to give

$t = \frac{(m_{water}+m_{salt})C_p \Delta T}{Q/t}$

This equation can be set up for each container, and the ratio of the times it takes to reach the boiling point can be found by dividing one equation by the other, which conveniently eliminates some of the variables. At a constant heating rate for each container, that ratio becomes the following:

$\frac{t_1}{t_2} = \frac{(m_{water}+m_{salt1})C_{p1} \Delta T_1}{(m_{water}+m_{salt2})C_{p2}\Delta T_2}$

This means that the mass of salt in each container, the specific heat of each solution, and the temperature rise of each solution, must be known for the specific mixtures being tested before this question can be answered.

$\endgroup$
1
  • $\begingroup$ Thanks for your detailed answer! $\endgroup$ Oct 8, 2023 at 21:20

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.