---
title: "Scale N: reading at 150°C, equal reading"
subject: "Fundamental of Thermodynamics & Heat Transfer"
chapter: 1
key: "semester_2/fundamental_of_thermodynamics_and_heat_transfer:new-scale-n-150c-same-reading"
source: https://www.bctengineer.com/q/semester_2/fundamental_of_thermodynamics_and_heat_transfer/new-scale-n-150c-same-reading
site: BCT Engineering
---

# Scale N: reading at 150°C, equal reading

Fundamental of Thermodynamics & Heat Transfer · Chapter 1: Introduction

- Asked in: 2072 Magh, 6 marks
- Video: [Thermodynamics Problems | Temperature 3 | BTD](https://www.youtube.com/watch?v=mrx-aATWBB0) — Engineering Xplained
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_2/fundamental_of_thermodynamics_and_heat_transfer/new-scale-n-150c-same-reading
- Whole chapter: https://www.bctengineer.com/md/semester_2/fundamental_of_thermodynamics_and_heat_transfer/chapter-1

## Question

A new scale N of temperature is devised in such a way that the freezing point of ice is 100°N and boiling point is 400°N. What is the temperature reading on this new scale when the temperature is 150°C? At what temperature, both the celsius and new temperature scale reading would be the same?

## Short answer

Linear relation N = 100 + 3C. At 150°C, N = 550°N. Setting N = C gives C = -50; both scales read the same at -50°.

## Answer

**Given:** ice point 100 °N (0 °C) and steam point 400 °N (100 °C), linear scale.

**Relation:** (N − 100)/(400 − 100) = C/100  
N = 100 + 3C

#### (a) Reading at 150 °C
N = 100 + 3(150) = 100 + 450 = **550 °N**

#### (b) Temperature where both readings are equal
Put N = C:
C = 100 + 3C  
−2C = 100  
C = −50

**Answer: 150 °C = 550 °N; both scales read the same at −50° (−50 °C = −50 °N).**

Check: N = 100 + 3(−50) = −50. Correct.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Which relation links N and C for this scale?
   A. N = 100 + 3C
   B. N = 3C
   C. N = 100 + C/3
   D. N = 400 - C
   Answer: A. From (N - 100)/300 = C/100, N = 100 + 3C. (Key point: Scale relation)

2. What is the reading on the N scale at 150 °C?
   A. 450 °N
   B. 650 °N
   C. 550 °N
   D. 350 °N
   Answer: C. N = 100 + 3(150) = 550 °N. (Key point: Reading at 150 °C)

3. How is the temperature at which both scales read the same found?
   A. Put C = 0
   B. Put N = C in N = 100 + 3C
   C. Put N = 400
   D. Put N = 3C
   Answer: B. Setting N = C gives C = 100 + 3C, so C = -50. (Key point: Equal readings)

4. At what value do both scales read the same?
   A. 100
   B. 50
   C. 0
   D. -50
   Answer: D. -2C = 100 gives C = -50, and N = 100 + 3(-50) = -50. (Key point: Equal reading result)

## Related in Fundamental of Thermodynamics & Heat Transfer

- [New temperature scale N conversion](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Anew-scale-n-temperature-conversion) — Fundamental of Thermodynamics & Heat Transfer, chapter 1

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