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 100 ∘Z to the Celsius scale.

C) Convert 100 ∘Z to the Kelvin scale.

Answer 1

Boiling point of nitrogen = T₁ = -195.8 ^oC

Melting point of iron = T₂ = 1538 ^oC

On the Z scale,

Boiling point of nitrogen = Z₁ = 0 ^oZ

Melting point of iron = Z₂ = 1000 ^oZ

Let us take the conversion from Celsius scale to Z scale as,

Z = AT + B,

where,

Z = temperature in Z scale,

T = temperature in Celsius scale,

A and B are constants.

For the boiling point of nitrogen,

Z₁ = AT₁ + B

0 = A(-195.8) + B

195.8A = B

For the melting point of iron,

Z₂ = AT₂ + B

1000 = A(1538) + B

1000 = 1538A + 195.8A

A = 0.5768

B = 195.8A

B = 112.937

Z = 0.5768T + 112.937

Boiling point of water = T₃ = 100 ^oC

Boiling point of water on Z scale = Z₃

Z₃ = 0.5768T₃ + 112.937

Z₃ = (.5768)(100) + 112.937

Z₃ = 170.617 ^oZ

Z₄ = 100 ^oZ

Equivalent temperature on celsius scale of 100 ^oZ = T₄

Z₄ = 0.5768T₄ + 112.937

100 = 0.5768T₄ + 112.937

T₄ = -22.43 ^oC

Converting to Kelvin scale,

T₄ = -22.43 ^oC = -22.43 + 273 K = 250.57 K

A) Boiling point of water on the Z scale = 170.617 ^oZ

B) 100 ^oZ = -22.43 ^oC

C) 100 ^oZ = 250.57 K