10 kg of water at a temperature of 90 ° C Willie casserole where they have 2 kg of water at 30 ° C

10 kg of water at a temperature of 90 ° C Willie casserole where they have 2 kg of water at 30 ° C Determine the set water temperature after moving them.

Let’s write the heat balance equation Q1 = Q2;

Q1 = cm1 (t1 – θ); Q2 = cm2 (θ – t2).

Q1 – the amount of heat given off by hot water to cold water;

Q2 – the amount of heat received by cold water from hot water;

с – specific heat capacity of water, m1 and m2 mass of hot and cold water;

θ is the temperature of the mixture, t1 and t2 are the temperatures of hot and cold water;

cm1 (t1 – θ) = cm2 (θ – t2); m1t1 – m1θ = m2θ – m2t2; m2θ + m1θ = m1t1 + m2t2; θ = (m1t1 + m2t2) / (m2 + m1);

θ = (10kg ∙ 90⁰С + 2kg ∙ 30⁰С) / (2kg + 10kg) = 960kg ∙ ⁰С / 12kg = 80⁰С.

Mix temperature: 80⁰С.