Question

How much heat must be extracted from 750 mL of white wine to cool it from 25 °C to 13 °C, if the wine is 9.6% ethanol by weight? Assume the wine can be treated as an aqueous solution of ethanol, with no other components. The molar heat capacity of water is 75.4 J/mol K and of ethanol is 112.1 J/mol K. [Bonus: Show that this corresponds to a wine that is 12% alcohol by volume, or ABV. Clearly state sources for any data used.]

Answer 1

Specific heats are calculated based on the mass:

cp water = 75.4 J / mol * K * (1 mol / 18 g) = 4.18 J / g * ° C

cp ethanol = 112.1 / 46 = 2.44 J / g * ° C

The cp of the mixture is calculated:

cp mix = (0.096 * 2.44) + (0.904 * 4.18) = 4.01 J / g * ° C

The heat required to withdraw is calculated:

q = m * cp * ΔT = 750 g * 4.01 * (13 - 25) = - 36090 J

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