Calculate the ratio of the masses of alcohol and gasoline in the mixture, the specific heat of combustion

Calculate the ratio of the masses of alcohol and gasoline in the mixture, the specific heat of combustion of which is qo = 38 MJ / kg. The specific heat of combustion of gasoline is qb = 44 MJ / kg, and the specific heat of combustion of alcohol is qc = 26 MJ / kg.

Given:

q = 38 MJ / kg is the specific heat of combustion of a mixture of alcohol and gasoline;

q1 = 44 MJ / kg is the specific heat of combustion of gasoline;

q2 = 26 MJ / kg is the specific heat of combustion of alcohol.

It is required to determine n1 and n2 – the ratio of the masses of alcohol and gasoline in the mixture.

Let m be the total mass of the mixture, m1 the mass of gasoline in the mixture, and m2 the mass of alcohol in the mixture. Then we have:

q * m = q1 * m1 + q2 * m2.

Since m1 + m2 = m (the total mass is equal to the sum of the masses of the components in the mixture). we get:

q * m = q1 * (m – m2) + q2 * m2;

q * m = q1 * m – q1 * m2 + q2 * m2;

q * m – q1 * m = q2 * m2 – q1 * m2;

m * (q – q1) = m2 * (q2 – q1);

m2 / m = (q – q1) / (q2 – q1) = (38 – 44) / (26 – 44) = (-6) / (-18) = 6/18 = 0.33 is the ratio of the mass of alcohol;

m1 / m = 1 – m2 / m = 1 – 0.33 = 0.67 is the ratio of the mass of gasoline.

Answer: the ratio of the mass of alcohol is 0.33, the ratio of the mass of gasoline is 0.67.