A certain material is in a room at 27°C. If the absolute temperature (K) of the material is tripled, its resistance doubles. (Water freezes at 273 K.) What is the value for alpha (a) the temperature coefficient of resistivity?
0.0050 (°C)−1
To find the value of alpha (temperature coefficient of resistivity, α), we can use the given information.
The temperature coefficient of resistivity, α, relates the change in resistance (ΔR) of a material to the change in temperature (ΔT) using the formula:
α = (ΔR / R) / ΔT
Let's break down the given information and solve for α step by step:
1. The material is initially at 27°C, which corresponds to 27 + 273 = 300 K (since 0°C = 273 K).
2. When the absolute temperature (K) of the material is tripled, it becomes 3 times the initial temperature: 300 K x 3 = 900 K.
3. According to the given information, when the temperature is tripled, the resistance doubles. Let's say the initial resistance is denoted as R0, and the final resistance is denoted as R.
We can write this relationship as:
R = 2R0
4. Now, let's calculate the change in resistance (ΔR) and the change in temperature (ΔT) to substitute into the formula for α:
ΔR = R - R0 = 2R0 - R0 = R0
ΔT = T - T0 = 900 K - 300 K = 600 K
5. Finally, we can substitute the values into the formula for α:
α = (ΔR / R) / ΔT = (R0 / 2R0) / 600 K = 1 / (2 × 600 K) = 1 / 1200 K
Therefore, the value for alpha (a), the temperature coefficient of resistivity, is 1 / 1200 K.