# How many degrees will 200g of water heat up if it receives all the energy released when 2kg

How many degrees will 200g of water heat up if it receives all the energy released when 2kg of copper cools down from 100 to 40 ° C?

mw = 200 g = 0.2 kg.

Cw = 4200 J / kg * ° C.

tm1 = 100 ° C.

tm2 = 40 ° C.

mm = 2 kg.

Cm = 400 J / kg * ° C.

Qw = Qm.

Δtв -?

Let us express the amount of heat Qm that is released during the cooling of copper according to the formula: Qm = mm * Cm * (tm1 – tm2), where mm is the mass of copper, C is the specific heat capacity of copper, tm1, tm2 are the initial and final temperatures during cooling.

The amount of heat Qw required for heating water is expressed by the formula: Qw = mw * Cw * Δtw, where mw is the mass of heated water, Cw is the specific heat capacity of water, Δtw is the increase in water temperature.

mw * Cw * Δtw = mm * Cm * (tm1 – tm2).

Δtw = mm * Cm * (tm1 – tm2) / mw * Cm.

Δtw = 2 kg * 400 J / kg * ° C * (100 ° C – 40 ° C) / 0.2 kg * 4200 J / kg * ° C = 57 ° C.

Answer: the water will heat up by Δtw = 57 ° C.

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