Temperature Scales

There are three main temperature scales, Fahrenheit , Celsius, and Kelvin all named after the scientists who originated the scales. In certain contexts, one scale might be more appropriate to use than another scale and there are linear formulas that allow you to convert from one system to another.

To convert from Celsius to Fahrenheit, the equation is

F = (9/5)C + 32,

where F stands for the temperature measured in Fahrenheit and C stands for the temperature measured in Celsius. Is there a temperature T so that the temperature measured in degrees Fahrenheit is equal to the temperature measured in degrees Celsius? To find this temperature (if it exists) we need to solve the system of linear equations

F = (9/5)C + 32

and

F = C.

Graph these two lines with Celsius as the x-coordinate and Fahrenheit as the y-coordinate. Solve this system (if possible). If there is a temperature that is the same in both Celsius and Fahrenheit label it on your graph. If it is not possible to solve this system, explain why it is impossible to find a point of intersection.

To convert from Celsius to Kelvin, the equation is

K = 273+C

where K stands for the temperature measured in Kelvin and C stands for the temperature measured in Celsius. Is there a temperature T so that the temperature measured in degrees Kelvin is equal to the temperature measured in degrees Celsius? To find this temperature (if it exists) we need to solve the system of linear equations

K = 273+C

and

K = C.

Graph these two lines with Celsius as the x-coordinate and Kelvin as the y-coordinate. Solve this system (if possible). If there is a temperature that is the same in both Celsius and Kelvin, label it on your graph. If it is not possible to solve this system, explain why it is impossible to find a point of intersection.

To convert from Kelvin to Fahrenheit, we need to combine the equation

F = (9/5)C+32,

with the equation

K = 273+C

to get a formula involving just Kelvin and Fahrenheit. Solve the second equation K = 273+C for C and substitute this into the equation for Fahrenheit for C. After simplifying, you should have an equation involving only F and K. Using this new equation, we can ask the question of whether or not there is a temperature T so that the temperature measured in degrees Fahrenheit is equal to the temperature measured in degrees Kelvin? To find this temperature (if it exists) we need to solve the system of linear equations using the equation you found involving F and K and the equation F = K.

Graph these two lines with Kelvin as the x-coordinate and Fahrenheit as the y-coordinate. Solve this system (if possible). If there is a temperature that is the same in both Kelvin and Fahrenheit label it on your graph. If it is not possible to solve this system, explain why it is impossible to find a point of intersection.