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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. what is the boiling point of water on the z scale?

Respuesta :

Edufirst
Answer: 170.6°Z

Explanation:


1) Since you are given two pair of points, you have to assume a linear relation ship to find the new scale.

2) Boiling point of nitrogen is -195.8° C and  0° Z

⇒ (- 195.8, 0)


3) Melting point of iron is 1538° C and 1000° Z


⇒ (1538, 1000)


4) Find the linear equation between C and Z:


[tex] \frac{1000 - 0}{1538-(-195.8)} = \frac{Z-0}{C-(-195.8)} [/tex]


Solving for Z:

1000 (C + 195.8) = Z (1538 + 195.8) ⇒

1000 C + 195,800 = 1,733.8Z ⇒

Z = (1,000/1,733.8)C + 195,800/1,733.8


4) Boiling point of water is 100°C ⇒ replace C = 100 in the equation


Z = (1,000 / 1733.8) (100) + 195,800/1,733.8 = 170.6°Z

okpalawalter8

The boiling point of water on the z scale is mathematically given as

Z= 170.6°Z

What is the boiling point of water on the z scale?

Question Parameter(s):

the boiling point of nitrogen 0 ∘z and the melting point of iron 1000 ∘z

Generally, the equation for the relationship between C and Z is mathematically given as

[tex]\frac{1000 - 0}{1538-(-195.8)} = \frac{Z-0}{C-(-195.8)}[/tex]

Therefore

1000 (C + 195.8) = Z (1538 + 195.8)

1000 C + 195,800 = 1,733.8Z

Z = (1,000/1,733.8)C + 195,800/1,733.8

In conclusion, with boiling point of water as 100°C

Z = (1,000 / 1733.8) (100) + 195,800/1,733.8

Z= 170.6°Z

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