Question

"Today's temperature of 42 in Chicago set a record high for the month of August." Which temperature scale is being used? What would be the corresponding temperature on the other two scales?

Answer 1

Celsius scale; 315 K;
`107.6^(\circ)F`

Step-by-step explanation:

The scale used to express the temperature in Chicago in this problem is the Celsius scale.

The Celsius degree is indicated with the symbol
`^(\circ)C`. The Celsius scale is based on two points:

- The freezing point of water, placed at
`0^(\circ)C`

- The boiling point of water, placed at
`100^(\circ)`

However, there are two more temperature scales that are widely used:

- The Kelvin scale: the Kelvin scale is based on the concept of absolute zero, which is the temperature at which particles in matter stop moving, and it is indicated with
`0 K` (zero Kelvin). The expression to convert a temperature from Celsius degree to Kelvin is

`T(K)=T(^(\circ)C)+273`

In this case, the temperature in Chicago in Celsius scale is

`T(^(\circ)C)=42^(\circ)C`

So the temperature in Kelvin is

`T(K)=42+273=315 K`

- The Fahrenheit scale: the Fahrenheit degree is indicated with
`^(\circ)F`. The expression to convert a temperature from Celsius degree to Fahrenheit degree is

`T(^(\circ)F)=(9)/(5)T(^(\circ)C)+32`

In this case, the temperature in Chicago in Celsius scale is

`T(^(\circ)C)=42^(\circ)C`

So the temperature in Fahrenheit is

`T(^(\circ)F)=(9)/(5)\cdot 42 + 32=107.6^(\circ)F`