A thermometer with an arbitrary scale S, of equal division registers -30oS at the ice point and +90oS at the steam point. Calculate the Celsius temperature ...

A thermometer with an arbitrary scale S, of equal division registers -30oS at the ice point and +90oS at the steam point. Calculate the Celsius temperature corresponding to 60oS

Answer Details

To convert from the arbitrary scale S to Celsius, we need to use the following formula: C = (S - 32) x 5/9 First, we need to find the conversion factor between S and Fahrenheit: (Smax - Smin)/(Fmax - Fmin) = (90 - (-30))/(212 - 32) = 120/180 = 2/3 So, for a given temperature T on the arbitrary scale, the corresponding temperature on the Fahrenheit scale is: T_F = (T - Smin) x (Fmax - Fmin)/(Smax - Smin) + Fmin = (T - (-30)) x 180/120 + 32 = (T + 30) x 3/2 + 32 = 1.5T + 77 To convert 60 on the arbitrary scale to Celsius, we first need to find the corresponding temperature on the Fahrenheit scale: 60_S = 1.5 x 60 + 77 = 167 Then, we use the Celsius conversion formula: C = (F - 32) x 5/9 = (167 - 32) x 5/9 = 135 x 5/9 = 75.0°C Therefore, the answer is 75.0oC.