In the Sahara desert, the temperature of X °C was recorded. If the scale used had been Fahrenheit, the reading would be 72 units higher. Determine the value of these temperatures.

The temperature can be measured with a mercury thermometer. In this type of thermometer, the temperature is the length ℓ of a capillary column, measured from a common origin. It is verified that ℓ = 2.34 cm, when the thermometer is in thermal equilibrium with melting ice, and ℓ = 12.34 cm when thermal equilibrium is with boiling water (in an environment at which atmospheric pressure is 1 atm).
a) Determine the equation of this thermometer;
b) Calculate the length of the column of mercury when the temperature is θ = 25 °C;
c) Calculate the temperature of the environment when ℓ = 8.84 cm.

Determine:
a) The temperature with the same numerical value on the Celsius and Fahrenheit scales;
b) The temperature with the same magnitude but with opposite signs on the Celsius and Fahrenheit scales.

One thermometer has the Celsius and Fahrenheit scales. Determine the temperature variation, on the Fahrenheit scale, which corresponds to a change of 20 °C.

The difference between the values indicated in a thermometer in the Fahrenheit scale and another in the Celsius scale are equal to 40 for the same temperature. What are the temperatures read in the two thermometers?