# Solid in Liquid Heat Transfer (Temperatures/Entropy Changes)

Suppose we have a solid of temperature $$T_s$$ and heat capacity $$C_p$$ submerged into a pool of water that has temperature $$T_w$$.

If $$T_s \gt T_w$$ and the pressure of the isolated pool-solid system is constant, how much heat will the solid lose, how much heat will the pool gain and what will the entropy change be for every part?

Edit I do understand that the format of the question resembles that of a plain exercise. However, aid in a question as such will mostly help me understand what kind of a process this heat transmission is and how it could be described mathematically. That said, I have indeed worked on the question and reached a certain point of progress but would appreciate some help.

• Please show us what you got so far. Also, please understand that the final state and the changes in temperature and entropy of the solid and the water for this irreversible process are independent of the details of the process. – Chet Miller Aug 12 at 23:55
• Here is a link to a cookbook recipe for determining the change in entropy for an irreversible process such as this: physicsforums.com/insights/grandpa-chets-entropy-recipe – Chet Miller Aug 12 at 23:57
• For a start, thank you for your answer. Well, concerning my progress, from the formula δq=Cp*dT (for the solid), I got via integration that Δq=Cp*(Ts'-Ts)<0, where Ts' is the occuring temperature of the solid after its immersion in the lake. Moreover, I know that for the solid dS=δq/Τ which, via integration, gives the formula ΔS=Cp=lnT – WannaBeScientist Aug 13 at 0:37
• I assume that you are looking for the steady state answer? If not, are you looking for a function of heat transfer vs. time? – David White Aug 13 at 0:45
• Well, @ChetMiller, I did grasp the idea, so thank you for your analysis. It is evident that by use of these formulas and the energy balance equations, I shall be able to determine the final temperatures thus solving the problem. – WannaBeScientist Aug 17 at 12:59

First the general case: When matter is heated or cooled under constant pressure, the amount of heat is $$Q = \Delta H$$ and the entropy change is $$\Delta S = \int \frac{dH}{T}$$ In the special case that there is no phase change and the heat capacity is constant, then $$Q = m\, C_P (T_f - T_i)$$ and $$\Delta S = m\, C_P \ln\frac{T_f}{T_i}$$ where $$T_i$$ and $$T_f$$ is the initial and final temperature. The last two equations will solve your problem. First write the energy balance to find out what is the final temperature. Once you know the final temperature, calculate the heat and entropy.