At an ambient temperature of 20º C, each kg of a human body emits approximately 1.6 J of heat in 1 s.

At an ambient temperature of 20º C, each kg of a human body emits approximately 1.6 J of heat in 1 s. How many degrees can 1 liter of water be heated if you transfer to the water the warmth that a student weighing 49 kg emits during a 45-minute lesson.

t1 = 1 s.

Q1 = 1.6 J.

Vw = 1 l = 0.001 m3.

ρw = 1000 kg / m3.

Sv = 4200 J / kg * ° C.

mm = 49 kg.

t = 45 min = 2700 s.

ΔT -?

Let us find the amount of thermal energy Q that the student emits during one lesson: Q = t * Q1 * mm.

To heat water, the required amount of heat Q is expressed by the formula: Q = Sv * mw * ΔT.

We express the mass of water mw by the formula: mw = Vw * ρw.

Q = Sv * Vw * ρw * ΔT.

t * Q1 * mm = Sv * Vw * ρw * ΔT.

ΔT = t * Q1 * mm / Sv * Vw * ρw.

ΔT = 2700 s * 1.6 J * 49 kg / 4200 J / kg * ° C * 0.001 m3 * 1000 kg / m3 = 50.5 ° C.

Answer: water can be heated by ΔT = 50.5 ° C.