What mass of water needs to be heated to 90 degrees Celsius with the amount of heat obtained

What mass of water needs to be heated to 90 degrees Celsius with the amount of heat obtained during the combustion of 200 g of alcohol?

Δt = 90 ° C.

C = 4200 J / kg * ° C.

q = 2.7 * 10 ^ 7 J / kg.

msp = 200 g = 0.2 kg.

mv -?

The amount of thermal energy Qw, which is necessary for heating water, is expressed by the formula: Qw = C * mw * Δt, where C is the specific heat capacity of water, mw is the mass of heated water, Δt is the change in water temperature.

The amount of thermal energy that is released during the combustion of alcohol is expressed by the formula: Qsp = q * msp, where q is the specific heat of combustion of alcohol, msp is the mass of alcohol that burned.

Since there are no losses of heat energy, then Qsp = Qw.

q * msp = C * mw * Δt.

mw = q * msp / C * Δt.

mw = 2.7 * 10 ^ 7 J / kg * 0.2 kg / 4200 J / kg * ° C * 90 ° C = 14.3 kg.

Answer: you can heat water with a mass of mw = 14.3 kg with alcohol.