The steel bar was immersed in a vessel containing m = 20 kg of water, the temperature of which is t = 90∘C.

The steel bar was immersed in a vessel containing m = 20 kg of water, the temperature of which is t = 90∘C. What temperature will be established in the vessel if the water gives off Q = 840 kJ of heat during cooling? Express the answer in degrees Celsius, rounded to the nearest whole number. Specific heat capacity of water c = 4200 J / (kg⋅∘C).

Given:

m = 20 kilograms is the mass of water in the vessel;

c = 4200 J / (kg * C) – specific heat capacity of water;

Q = 840 kJ = 840 * 10 ^ 3 Joules – the amount of heat given off by water during cooling.

T1 = 90 degrees Celsius – the initial water temperature.

It is required to determine the final water temperature T2 (degrees Celsius).

Q = c * m * (T1 – T2);

Q = c * m * T1 – c * m * T2

c * m * T2 = c * m * T1 – Q

T2 = (c * m * T1 – Q) / (c * m) = T1 – Q / (c * m) =

= 90 – 840,000 / (4200 * 20) = 90 – 840,000 / 84,000 = 90 – 10 = 80 degrees.

Answer: the water temperature will be 80 degrees Celsius.