Difficult thermodynamics question (p. chem)

[notawretcheddrunk]

ok, here's a tricky brainteaser, whoever solves it is incredibly smart

uhh, actually, it's homework, and it seems pretty basic. Well, here it goes

"explain how liquid water can go from 25C/1 atm to 30C/1 atm in a process for which q<0"

I was thinking perhaps that since $$q=mc_p \Delta T$$, how can q be negative when the temperature change is positive? , maybe it's due to the specific heat, however the only other factor which effects cp is temperature right? Well since the tempreature change is already given, I'm not quite sure how one can say that it is due to cp, me thinks it shouldn't be.

I guess it has to do with internal energy, but how is it that q is not always dependent on temperature then when we are given the q equation? How can we explain the situation in terms of the heat equation (above).

 

[Bystander]

One post is more than enough to get peoples' attention --- just a point on etiquette for your future reference and use.

You have an initial state, and a final state. You get to pick the path. You can run it through diseased holy men, hit it with hammers, electrolyze it and combust the products, repeat Joule's experiment --- anything your little heart desires, so long as the sum of q for all steps along the path equals zero, and so long as you return to the 1 atm condition.

 

[notawretcheddrunk]

yeah i wasnt getting any answer so, i posted in the engineering forum also

so i guess it has to be due to cp then since

$$q_p= \int C_p(T) dT$$

and the overall temperature change is positive, right? i need a mathematical validation.

 

[Bystander]

"Fourth Law of Thermodynamics:" "Guessing" is evidence of lack of understanding.

Where in the problem statement does it state that you are to find a reversible path?

 

[notawretcheddrunk]

i see what you mean, well in the engineering forum they suggested that the temperature could be raised by doing work on the system, this makes sense. That's probably the answer. thanks for your help, you are definitely right in that it may or not be reversible path, also i learned that cp or cv can not be negative.