# The temperature a liquid would boil: question incorrectly formulated or not?

I have met a question in a high school physics book which I think is incorrectly formulated.

The question is this: In order to reach boiling temperature, a certain liquid requires twice the amount of energy compared to water. At what temperature does it boil?

The book says the answer is 200 Celsius.

It seems wrong to me because it does not mention the specific heat of the liquid. Knowing only the amount of heat provided is not enough to know the temperature it will reach, I think.

Am I wrong or is the book wrong?

• The book is wrong, and your assessment is correct. Jan 20 '16 at 13:08
• I agree with Chester. Also it doesn't state the starting temperature or the volume of liquid. Terrible terrible question. Jan 20 '16 at 13:19
• Wow... someone's having fun downvoting answers Jan 20 '16 at 20:39

The book is wrong in the sense that it has made a lot of assumptions without actually accounting for all of them. So you are right that the question has incomplete information.

The inaccuracies in the question are as follows:

1. In such questions, you must refer to the principle of calorimetry. $$m_1s_1t_1=H=m_2s_2t_2$$ where $H=$heat absorbed by the body,
$m=$mass of that body,
$s=$specific heat of the body,
$t=$change in temperature of body and
the indices $1,2$ refer to the two bodies in contact
2. The question does not mention the mass of the liquid, whether it is the same as that of water or anything else.
3. In a similar manner, the question does not mention the specific heat of the liquid, whether it is the same as that of water or not.
4. Also no mention of initial temperature of liquid.

So the question is quite vague.

• I think it is plausible to assume that the initial temperature is room temperature for both water and the other liquid, and also that the masses are the same. My main problem is with the specific heat. Jan 20 '16 at 15:20
• @thedude I agree with you. But as you have said it yourself... "plausible to assume"..... such assumptions are actually very crucial in thermodynamics. Jan 20 '16 at 15:21
• Further specific heats do have a correlation with vaporisation temp hence we can not actually assume to to be same...A paradox. Jan 22 '16 at 13:26

I'd say the book is 50% wrong. For this problem, you have to assume that the specific heat is the same (or that the boiling point is the same). But either way, the problem is badly formulated. In order to solve it, you have to use the fact that this is a textbook problem and therefore must be solvable (and that's a really un-clean way of solving it).

I guess what the book is saying is something like this: the second liquid, regardless of specific heat, takes twice the amount of energy to boil as compared to water.

Another thing I don't like about the answer is that it is in Celsius, not Kelvin. Whenever thermodynamics is involved, Kelvin must always be used.

• Hey! Some of us still prefer Rankine! Jan 20 '16 at 13:37
• If you don't know the boiling temperature, does it make sense to say that "regardless of specific heat" it takes twice the amount of energy to boil as compared to water? Jan 20 '16 at 15:18
• Well, if you don't take specific heat into account, then double the energy will double the heat. As for the Rankine scale, eh, I would rank it as second to Kelvin, just for one reason: I find it convenient to have 0 be the freezing point of water and 100 to be the boiling point. Apart from that, the two are absolutely equal. Jan 20 '16 at 18:25

Along with all the other reasons posted, it's flat-out absurd to think that requiring double the thermal energy would somehow change the boiling point from 100 to 200 $^\circ C$ . Maybe from X to 2*x Kelvins, but even then the heat of vaporization appears to have been ignored.

Edit: as thedude points out, the energy to reach boiling temperature is independent of the heat of vaporization, although the heat required to actually boil does depend on that value.

• Vaporization heat is not relevant, because the question is about reaching boiling temperature, it is not about the boiling itself. But you are right. If the other liquid had the same specific heat as water, and the same mass, then double the heat would produce double the temperature variation, not double the final temperature. Yes? Jan 20 '16 at 15:26