In an aluminum saucepan weighing 1.5 kg, there is 800 grams of water at a room temperature of 20 degrees

In an aluminum saucepan weighing 1.5 kg, there is 800 grams of water at a room temperature of 20 degrees, how much boiling water you need to add to the pan to get water at a temperature of 45 degrees.

mk = 1.5 kg.

Sc = 920 J / kg * ° C.

Sv = 4200 J / kg * ° C.

mw = 800 g = 0.8 kg.

t1 = 20 ° C.

t2 = 100 ° C.

t3 = 45 ° C.

m -?

When adding boiling water, it will give off the amount of heat Qk, which will go to heat the water and the aluminum pan Q.

Qk = Q.

Qk = Sv * m * (t2 – t3).

Q = Sv * mv * (t3 – t1) + Ck * mk * (t3 – t1).

Sv * m * (t2 – t3) = Sv * mv * (t3 – t1) + Ck * mk * (t3 – t1).

m = (Sv * mw * (t3 – t1) + Ck * mk * (t3 – t1)) / Sv * (t2 – t3).

m = (4200 J / kg * ° C * 0.8 kg * (45 ° C – 20 ° C) + 920 J / kg * ° C * 1.5 kg * (45 ° C – 20 ° C)) / 4200 J / kg * ° C * (100 ° C – 45 ° C) = 0.51 kg.

Answer: the mass of boiling water is m = 0.51 kg.