A faulty thermometer reads 1.05°C at the ice point and 106°C at the steam point. What will this thermometer read when the standard thermometer reads -0.5°C?

To determine the reading on the faulty thermometer when the standard thermometer measures -0.5^ C, we first establish a linear relationship between the two scales using their fixed points. Step 1: Identify the fixed points for both thermometers. Standard Celsius Thermometer (T_s): Ice point (T_s,ice) = 0^ C Steam point (T_s,steam) = 100^ C Faulty Thermometer (T_f): Reading at ice point (T_f,ice) = 1.05^ C (when T_s = 0^ C) Reading at steam point (T_f,steam) = 106^ C (when T_s = 100^ C) Step 2: Set up the conversion formula. The relationship between two linear temperature scales can be expressed as: T_s - T_s,iceT_s,steam - T_s,ice = T_f - T_f,iceT_f,steam - T_f,ice Step 3: Substitute the known fixed points into the formula. (T_s - 0)/(100 - 0) = (T_f - 1.05)/(106 - 1.05) (T_s)/(100) = (T_f - 1.05)/(104.95) Step 4: Rearrange the formula to solve for T_f. T_f - 1.05 = (104.95)/(100) × T_s T_f = ((104.95)/(100)) T_s + 1.05 T_f = 1.0495 T_s + 1.05 Step 5: Substitute the given standard temperature (T_s = -0.5^ C) into the derived formula. T_f = 1.0495 × (-0.5^ C) + 1.05^ C Step 6: Calculate the value of T_f. T_f = -0.52475^ C + 1.05^ C T_f = 0.52525^ C Rounding to three decimal places, the temperature on the faulty thermometer is: T_f ≈ 0.525^ C The temperature measured by the faulty thermometer when the original thermometer measures -0.5^ C will be 0.525^ C.