How much alcohol needs to be burned to heat 0.5 ton water from 200 ºС to 700 ºС?

How much alcohol needs to be burned to heat 0.5 ton water from 200 ºС to 700 ºС? (Specific heat of combustion of alcohol 27 ∙ 10 ^ 6 J / kg, specific heat of water 4200 J / kg. ºС).

Let’s convert the mass of water to the SI system (in kg). 1 t = 1000 kg => 0.5 t = 500 kg.

Let us write down the formula for the amount of heat when the body is heated: Q = c * mw * (t2 – t1), where c is the specific heat capacity of water, mw is the mass of water.

Let us write down the formula for the amount of heat during combustion: Q = λ * mс, where λ is the specific heat of combustion of alcohol, mс is the mass of alcohol.

Since you need to find out how much alcohol you need to burn in order to heat the water, the same amount of heat should be released in both cases. Let’s equate expressions.

s * mw * (t2 – t1) = λ * mc;

Substitute and solve the corresponding equation:

4200 * 500 * (700 – 200) = 27 * 10 ^ 6 * mc;

mc ≈ 38.9 kg.

Answer: 38.9 kg.