An electric heater with a resistance of 200 Ohm is used to heat 440 g of milk. The electric heater is plugged

An electric heater with a resistance of 200 Ohm is used to heat 440 g of milk. The electric heater is plugged into a 220 V network. How long does it take for the milk in the vessel to heat up to 55 ° C? The specific heat capacity of milk is assumed to be 3900 J / (kg · ° С). Neglect heat exchange with the environment.

R = 200 ohms.

m = 440 g = 0.44 kg.

U = 220 V.

Δt = 55 ° C.

C = 3900 J / kg * ° C.

T -?

If the losses of thermal energy are neglected, then the entire amount of heat Qн, which is released in the heater, goes to heating the milk Qm: Qn = Qm.

An amount of heat is released in the heater, which can be expressed by the Joule-Lenz law: Qн = U2 * T / R.

The amount of heat Qm required for heating milk is expressed by the formula: Qm = C * m * Δt.

U2 * T / R = C * m * Δt.

Milk heating time will be determined by the formula: T = C * m * Δt * R / U ^ 2.

T = 3900 J / kg * ° * 0.44 kg * 55 ° C * 200 Ohm / (220 V) ^ 2 = 390 s = 6 min 30 s.

Answer: the milk will heat up after a time T = 390 s = 6 min 30 s.