The resistances of platinum wire at the ice and steam points are 0.75 ohm and 1.05 ohm respectively. Determine the temperature at which the resistance of th...

The resistances of platinum wire at the ice and steam points are 0.75 ohm and 1.05 ohm respectively. Determine the temperature at which the resistance of the wire is 0.90 ohm

Answer Details

The resistance of a wire changes as its temperature changes. This change in resistance can be used to measure the temperature. The relationship between temperature and resistance is described by the temperature coefficient of resistance (TCR), which is different for different materials. For platinum, the TCR is approximately 0.00392 per degree Celsius. To determine the temperature at which the resistance of the wire is 0.90 ohm, we can use the following formula: Rt = R0 (1 + αt) where: Rt is the resistance of the wire at temperature t R0 is the resistance of the wire at the ice point (0°C or 273.15K) α is the TCR for platinum (0.00392/°C) t is the temperature of the wire in Celsius We can use this formula to solve for t by plugging in the values given in the problem: 0.90 = 0.75 (1 + 0.00392t) 0.90/0.75 = 1 + 0.00392t 1.2 = 1 + 0.00392t 0.2 = 0.00392t t = 0.2/0.00392 t ≈ 51 Therefore, the temperature at which the resistance of the wire is 0.90 ohm is approximately 51°C, which corresponds to answer choice (B) 50.0°C.