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.
