On an alcohol lamp with an efficiency of 40%, 3 g of alcohol burns out every minute.

On an alcohol lamp with an efficiency of 40%, 3 g of alcohol burns out every minute. How long does it take to heat 1.5 liters of water on it from 10 ° C to a boil?

Efficiency:

η = (A / Q) * 100%, where η = 40% or 0.4; A – water heating; Q – alcohol burning.

A = Qw = C * m1 * (t2 – t1), where C = 4200 J / (K * kg), m1 = 1.5 kg (1.5 liters of water have a mass of 1.5 kg), t2 = 100 ºС , t1 = 10 ºС.

Q = q * m, q = 2.7 * 10 ^ 7 J / kg, m2 = m2.1 * t (m2.1 = 3 g or 0.003 kg).

η = С * m1 * (t2 – t1) / (q * m2.1 * t).

η * q * m2.1 * t = С * m1 * (t2 – t1).

t = С * m1 * (t2 – t1) / (η * q * m2.1).

Let’s perform the calculation:

t = 4200 * 1.5 * (100 – 10) / (0.4 * 2.7 * 10 ^ 7 * 0.003) = 17.5 minutes.