A potential difference of 10 V was applied to a uniform copper cylindrical conductor 40 m long.

A potential difference of 10 V was applied to a uniform copper cylindrical conductor 40 m long. What will be the temperature change of the conductor DT in 15 s? Neglect the change in the resistance of the conductor and the dissipation of heat during heating. (The resistivity of copper is 1.7 × 10–8 Ohm × m.)

The amount of heat spent on heating the body is equal to the product of the specific heat capacity of the substance, body weight and the difference between the final and initial temperatures.
Q = c * m * (t2-t1), where c is the specific heat capacity of the substance, m is the mass of the substance, t2 and t1 are the final and initial temperatures, respectively.
The amount of heat released during cooling is equal to that spent on heating according to the law of conservation of energy.
Specific heat of copper according to the reference book:
s = 385 J / (kg * K)
Δt = t2-t1.
Q = c * m * Δt
Expression for determining mass in terms of density:
m = V * ρ = S * l * ρ
Q = c * m * Δt = c * S * l * ρ * Δt
Power required for heating:
P = Q / τ, Q – where the amount of heat, τ – heating time.
Electric power is equal to:
P = U * I = U² / R
R = ρsp * l / S
find Q in terms of cardinality:
Q = P * τ = U² * τ * S / (ρsp * l)
Let’s equate Q:
c * S * l * ρ * Δt = U² * τ * S / (ρsp * l)
Let us express Δt from this expression:
Δt = U² * τ * S / ρsp * l * c * S * l * ρ = U² * τ / ρsp * l² * c * ρ
Let us substitute the numbers and find the change in temperature, taking into account that the density of copper is ρ = 8700 kg / m³.
Δt = U² * τ / ρsp * l² * c * ρ = 10² * 15 / (1.7 × 10–8 * 40² * 385 * 8700) = 16.4 K.
Answer: the temperature will increase by 16.4 K.