A faulty thermometer reads 5° C in melting ice and 95° C in stream. The correct temperature on absolute scale will be __________ K when the faulty thermometer reads 41° C.

Solution

Physics sir · 4 steps

The faulty scale is still linear, so match the fraction of the way from ice to steam on both scales.

1. Same fraction. On every linear scale, a given temperature sits the same fraction of the way from the ice point to the steam point. On this thermometer ice reads 5 and steam reads 95, so 90 divisions cover the 100 degrees of a correct Celsius scale.

   (T_C - 0)/(100 - 0) = (41 - 5)/(95 - 5)

2. Put in numbers. The right side is 36/90 = 0.4. So T_C = 0.4 × 100 = 40°C.
3. Convert to kelvin. T = 40 + 273.15 = 313.15 K.
4. So. The correct absolute temperature is about 313 K.

The common slip: 309. Subtracting the offset of 5 but not rescaling the 90 divisions to 100 gives 36°C, and so 309 K instead of 313 K.

The idea to keep. For any faulty scale, (reading - lower point)/(upper point - lower point) is the same on every scale. Get the true Celsius value first, then add 273.

Answer from the NTA final answer key. Solution by PrepWiser.