A faulty thermometer reads 1.05^ C at the ice point and 106^ C at the steam point. What is the temperature in Celsius when the faulty thermometer reads 30^ 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:

• Standard Celsius Thermometer:

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

• Faulty Thermometer (from the problem text):

  • Ice point ($T_{f,ice}$) = $1.05^\circ C$
  • Steam point ($T_{f,steam}$) = $106^\circ C$

The relationship between a temperature reading on the faulty scale ($T_f