How is heat transfer calculated for an aqueous salt solution?

I am familiar with using $$\dot{Q}=c_p\cdot\dot{m}\cdot\Delta T$$ to calculate the heat transfer rate of a fluid given a singular value for specific heat capacity (such as with water), but how do I go about calculating heat transfer rate for an aequeous solution such as $$MgCl_2 (aq)$$? Do I somehow use the heat capacities of both water and salt together?

• I'd be amazed if there's no expermintal resarch into taht. What did you find so far? – mart Sep 29 '20 at 14:52
• Check out solar systems - think some tried salt solutions but the disadvantage was corrosion iirc. – Solar Mike Sep 29 '20 at 18:46

1 Answer

The formula you are quoting is for estimating the heat exchange rate of a fluid that enters a control volume with rate $$\dot m$$ and has a change in temperature $$\Delta T$$.

If you know

• the mass rate of the solution
• the precise per weight ratio of your solution
• the heat capacity of the elements
• the temperature difference

And provided there are not endothermal or exothermal reactions, then its basically a pretty straight forward sum of the parts.

$$\dot{Q}_{total} = \dot{Q}_{water} + \sum _{i=1}^n \dot{Q}_{sub.1}$$ $$\dot{Q}_{total} = \dot{m}_{water}c_{p,water}\Delta T + \sum _{i=1}^n \dot{m}_{sub.i}c_{p,sub.i}\Delta T$$

However, you will find that in most cases, because $$c_p$$ of water is so much greater that most other substances and the weight percentage in most solutions is much greater, you probably don't need to bother.