A source with an EMF of 2.2 V and an internal resistance of 1 Ohm is closed with a copper wire, the mass

A source with an EMF of 2.2 V and an internal resistance of 1 Ohm is closed with a copper wire, the mass of which is 30.3 g. The resistance of the wire is equal to the internal resistance of the source. How many degrees will the wire heat up in 5 minutes? Specific heat of copper 378 J / kg * K

Circuit current:

I = E / (r + R), where E – ЄDC, r – internal resistance, R – wire resistance.

Power dissipated on external resistance:

P = R * I ^ 2.

The work of an electric current when current passes through a conductor:

W = r * I ^ 2 * t

Heat dissipated on the conductor:

Q = ΔT * m * c.

According to the law of conservation of energy:

W = Q;

r * I ^ 2 * t = mcΔT;

r * (E / (r + R)) ^ 2 * t = mcΔT;

ΔT = (r * (E / (r + R)) ^ 2 * t) / mc =

= (1 Ohm * (2.2 V / (1 Ohm +1 Ohm)) ^ 2 * 300 s) / (0.0303 kg * 378 J / kg * K) =

= (1 Ohm * 1.21 (V / Ohm) ^ 2 * 300 s) / (11.45 J / K) = 31.7 K.