determine at what temperature aluminum will have the same resistivity as tungsten does at 24 ∘c.,

At what temperature does aluminum have the same resistivity as tungsten? This is a question that has been asked by many scientists and engineers. The answer to this question is not so easy, but we will try our best to give an estimate for it. The resistivity of tungsten is known to be “α = μ/ρ” and the resistance at 24 ∘c. can be found by using the expression: R=μL, where L is length in meters (m) and ρ its resistivity expressed in ohms per meter (Ω·m). The value for α here is dependent on temperature. It was previously stated that as temperature increases from zero Kelvin (-273 ˚C), a metal’s resistivity decreases exponentially. This means that if we know the resistivities at two different temperatures, say 0 ˚C and 100 ˚C, then it follows that every time you double your starting temperature, you will need to multiply your resistivity by four. Hence, if the temperature of aluminum is given as 20 ˚C, then its resistance will be: R=μL=(0.003+0.0012)·(100*100)/((350-25)) = 0.008 Ω·m or about one thousandth that at 100 ˚C where it would have a value of 0.00805Ω·m (or 125 times greater). If we want to find out what this temperature is for tungsten so that they have equal resistivities, we can use the expression “R ∝ T” and substitute in α W = μ/ρ which gives us an answer of -213 ∘