Question

A demented scientist creates a new temperature scale, the “Z scale.” He decides to call the boiling point of nitrogen 0°Z and the melting point of iron 1000°Z.

a. What is the boiling point of water on the Z scale?

b. Convert 500°Z to degrees Celsius and to kelvins.

Short answer

a. The value of the boiling point of water on the Z scale is 170.7Z

b. The value of converting Convert 500°Z to kelvins and to degrees Celsius is ${671}^{o}C$and 944K

Step-by-step solution

Relation between the Z scale with celsius scale 

The equation of relation between the Z scale with Celsius scale is

$T_C=x{T}_Z+y$

where the x and y are constant.

At the boiling point, the value of $T_Z=0^{o}Z$and $T_C=-{196}^{o}C$

Applying all values

localid="1648466556502" $\begin{array}{rcl}{T}_C& =& x{T}_Z+y\\ -{196}^{o}C& =& x\left(0Z\right)+y\\ y& =& -{196}^{o}C\end{array}$

At the melting point, the value of $T_Z=-{1000}^{o}C$and $T_C={1538}^{o}C$

Applying all values

localid="1648466873103" $\begin{array}{rcl}{T}_C& =& x{T}_Z+y\\ {1538}^{o}C& =& x\left(1000Z\right)-{196}^{o}C\\ x& =& 1.734\end{array}$

Applying all values

localid="1648466891752" $\begin{array}{rcl}{T}_C& =& x{T}_Z+y\\ T_Z& =& \frac{T_C-y}{x}\\ T_Z& =& {\left(\frac{100+196}{1.734}\right)}^{o}C=170.7Z\end{array}$

Equationbetween the Z scale with celsius scale 

At $T_Z={500}^{o}Z$

Applying the values

$\begin{array}{rcl}{T}_C& =& x{T}_Z+y\\ T_C& =& (1.734)T_Z-196\\ T_C& =& {671}^{o}C\end{array}$

At kelvin point

Applying the value

role="math" localid="1648467049739" $\begin{array}{rcl}{T}_K& =& T_C+273\\ T_K& =& {671}^{o}C+273\\ & =& 944K\end{array}$