# Max temperature wire

1. Mar 28, 2015

### abro

Say I connect a wire to a power supply with a voltage V. The wire is a cilinder with a total surface area A, and resistance R. The wire will get hotter and hotter, and the temperature will increase linearly, according to the equation
R(T)=R(1+aT). It will give this heat off in the environment to heat up e.g. air molecules (P=λAdT/d ?, if so, what is d, assuming it reaches into infinity). And because the wire gets hotter, it will also emit electromagnetic radiation (P=eσ(T^4-T0^4 ?)
So here's my question, can we combine the electrical power input, together with the output factors such as internal and external heat and electromagnetic radiation to calculate the equilibrium temperature? Is there a formula for it? (I have seen a thread where it was derived when all the heat dissipitates through radiation)

2. Mar 28, 2015

### Staff: Mentor

Sure. Set heating power equal to power loss to the atmosphere, solve for T (probably numerically).
Regular thermal conductivity of air is often negligible, but you'll get convection. There are formulas to estimate its effect, but it depends on the environment of your cable (is it in free air? Horizontal, vertical, ...?).