A faulty thermometer reads 1.05°C at the ice point and 99.5°C at the steam point. What is the correct Celsius temperature when the faulty thermometer reads 50°C?

To solve this problem, we need to establish a relationship between the readings of the faulty thermometer and a standard Celsius thermometer.

First, let's identify the fixed points for both thermometers based on the problem statement:

• Standard Celsius Thermometer ($T_s$):

  • Ice point ($T_{s,ice}$) = $0^\circ C$
  • Steam point ($T_{s,steam}$) = $100^\circ C$

• Faulty Thermometer ($T_f$):

  • Ice point ($T_{f,ice}$) = $1.05^\circ C$ (This is the reading of the faulty thermometer when the actual temperature is $0^\circ C$)