1

Some time ago after discussing with my cooking friends I came up to a question:

Q: What makes water boil faster, adding salt a the begging or at the end of boiling?

A: Briefly, adding salt before makes water boil slightly faster (Salt and boiling speed )

That lead me to another question: the equality of energy consumption for 2 cases.

Let's imagine 2 experiments with fully isolated boiling pans. In first case we add salt at the end, in the second - we add salt before.

If the energy for dissolution salt is the same, but heat capacity of salted water is different from water, we get different energies for 2 experiments.

How is it possible to get different energy consumptions between 2 states of isolated system?

Example:

Assume we take 1 liter of water, 10 g of salt. At the beginning we have separate water and salt at 20 deg and the final state is a salty water at 80 deg (not to take into account difference in boiling temperatures) $$ Q = c\cdot m\cdot \Delta T $$

  • Heat capacity: $4182\; J\; kg^{-1}\;K^{-1}$ for water, $3898\; J\; kg^{-1}\;K^{-1}$ for salted water (35 g per 1 kg) (for $7.5^{\circ}C $)
  • Heat capacity: $880\; J\; kg^{-1}\;K^{-1}$ for salt
  • Integral molar heat of dissolution of salt in water for NaCl: $\Delta H_m = 4270\; J\;mole^{-1}$ for molar concentration of salt $0.2\; mole\;kg^{-1}$ that is $11.6\; g\; kg^{-1}$ $$ Q_{salt after} = 4182\cdot 1kg\cdot (80-20)^{\circ} + 880\cdot 0.010kg\cdot (80-20)^{\circ} + 4270\cdot 0.2 \approx 252\; kJ $$ $$ Q_{salt before} = 4270\cdot 0.2 + 3898\cdot 1kg\cdot (80-20)^{\circ} + 880\cdot 0.010kg\cdot (80-20)^{\circ} \approx 235\; kJ $$ Of cause the equation is not linear and coefficients change with changing in temperature. But it seems that there is still an important difference between consumed energy.
Shamil
  • 11
  • 'Check my work' questions are generally not welcome here. But I think there's an error on $\Delta H_m$. The molar mass of $\text{NaCl}= 58.443\text{ g/mol}$, so we get $\Delta H_m=4270/58.443=73$ $\text{ J/g}$ – Gert Aug 31 '20 at 14:21
  • Your first question is ambiguous. "Which is faster"? Which "what"? Are you trying to cook something as quickly as possible? Are you trying to bring the water to a boil as fast as possible? – David White Aug 31 '20 at 16:45
  • @Gert it is not 'check my work' question. It's that it is an interesting question and I passed pretty much time to search and write coefficients here, for it to be easy for the others to analyse the process. I also try to simplify the case as much as possible – Shamil Sep 01 '20 at 15:21
  • @Gert, you think it is easier to think about the problem with no support value or example? – Shamil Sep 01 '20 at 15:24
  • The function you're looking for is a state function: a change in its value depends only on state $2$ and state $1$, not on how you get from $1$ to $2$ ('path invariant'). This means the discrepancy is merely a calculation error on your part, not something 'conceptual'. That's why I call it a 'check my work' question. By all means do the calculation for a generic, non-numeric example. – Gert Sep 01 '20 at 15:45
  • @Gert, that's why I am asking a question. With different heat capacity coefficients there is something that also influences the energy besides heating. I am not asking to check my work or to criticize I am asking to point out what physical effect stands behind that makes the energies equal. – Shamil Sep 01 '20 at 15:55

0 Answers0