The graph between two temperature scales A and B is shown in Fig. Between upper fixed point and lower fixed point there are 150 equal division on scale A and 100 on scale B. The relationship for conversion between the two scales is given by

(a) $\frac{{\mathit{t}}_{\mathit{A}}-180}{100}=\frac{{\mathit{t}}_{\mathit{B}}}{150}$

(b) $\frac{{\mathit{t}}_{\mathit{A}}-30}{150}=\frac{{\mathit{t}}_{\mathit{B}}}{100}$

(c) $\frac{{\mathit{t}}_{\mathit{B}}-180}{150}=\frac{{\mathit{t}}_{\mathit{A}}}{100}$

(d) $\frac{{\mathit{t}}_B-40}{100}=\frac{{\mathit{t}}_{\mathit{A}}}{180}$

This is a multiple choice answer as classified in NCERT Exemplar

(b) Lowest point for scale A is 30⁰ and lowest point for scale B is 0⁰. Highest point for the scale A is 180⁰ and for scale B is 100⁰

$\frac{{\mathrm{t}}_{\mathrm{A}}-{\mathrm{L}\mathrm{E}\mathrm{P}}_{\mathrm{A}}}{{\mathrm{U}\mathrm{F}\mathrm{P}}_{\mathrm{A}}-{\mathrm{L}\mathrm{F}\mathrm{P}}_{\mathrm{A}}}=\frac{{\mathrm{t}}_{\mathrm{B}}-{\mathrm{L}\mathrm{F}\mathrm{P}}_{\mathrm{B}}}{{\mathrm{U}\mathrm{F}\mathrm{P}}_{\mathrm{B}}-{\mathrm{L}\mathrm{F}\mathrm{P}}_{\mathrm{B}}}$

$\frac{{\mathrm{t}}_{\mathrm{A}}-\mathrm{}30}{180-30}=\frac{{\mathrm{t}}_{\mathrm{B}}-0}{100-0}\mathrm{}\mathrm{}$

$\frac{t_A-30}{150}=\frac{t_B}{100}$ ,LFP= lower fixed point , UFP= upper fixed point $\propto \rho$

<p><span data-teams="true">This is a multiple choice answer as classified in NCERT Exemplar</span></p><p>(b) Lowest point for scale A is 30⁰ and lowest point for scale B is 0⁰. Highest point for the scale A is 180⁰ and for scale B is 100⁰</p><div><div><picture><source srcset="https://images.shiksha.com/mediadata/images/articles/1745477089phpXZoyET_480x360.jpeg" media="(max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/articles/1745477089phpXZoyET.jpeg" alt="" width="191" height="143"></picture></div><div><span contenteditable="false"> <math> <mfrac> <mrow> <mrow> <msub> <mrow> <mrow> <mi mathvariant="normal">t</mi> </mrow> </mrow> <mrow> <mrow> <mi mathvariant="normal">A</mi> </mrow> </mrow> </msub> <mo>-</mo> <msub> <mrow> <mrow> <mi mathvariant="normal">L</mi> <mi mathvariant="normal">E</mi> <mi mathvariant="normal">P</mi> </mrow> </mrow> <mrow> <mrow> <mi mathvariant="normal">A</mi> </mrow> </mrow> </msub> </mrow> </mrow> <mrow> <mrow> <msub> <mrow> <mrow> <mi mathvariant="normal">U</mi> <mi mathvariant="normal">F</mi> <mi mathvariant="normal">P</mi> </mrow> </mrow> <mrow> <mrow> <mi mathvariant="normal">A</mi> </mrow> </mrow> </msub> <mo>-</mo> <msub> <mrow> <mrow> <mi mathvariant="normal">L</mi> <mi mathvariant="normal">F</mi> <mi mathvariant="normal">P</mi> </mrow> </mrow> <mrow> <mrow> <mi mathvariant="normal">A</mi> </mrow> </mrow> </msub> </mrow> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mrow> <msub> <mrow> <mrow> <mi mathvariant="normal">t</mi> </mrow> </mrow> <mrow> <mrow> <mi mathvariant="normal">B</mi> </mrow> </mrow> </msub> <mo>-</mo> <msub> <mrow> <mrow> <mi mathvariant="normal">L</mi> <mi mathvariant="normal">F</mi> <mi mathvariant="normal">P</mi> </mrow> </mrow> <mrow> <mrow> <mi mathvariant="normal">B</mi> </mrow> </mrow> </msub> </mrow> </mrow> <mrow> <mrow> <msub> <mrow> <mrow> <mi mathvariant="normal">U</mi> <mi mathvariant="normal">F</mi> <mi mathvariant="normal">P</mi> </mrow> </mrow> <mrow> <mrow> <mi mathvariant="normal">B</mi> </mrow> </mrow> </msub> <mo>-</mo> <msub> <mrow> <mrow> <mi mathvariant="normal">L</mi> <mi mathvariant="normal">F</mi> <mi mathvariant="normal">P</mi> </mrow> </mrow> <mrow> <mrow> <mi mathvariant="normal">B</mi> </mrow> </mrow> </msub> </mrow> </mrow> </mfrac> </math> </span></div><div><span contenteditable="false"> <math> <mfrac> <mrow> <mrow> <msub> <mrow> <mrow> <mi mathvariant="normal">t</mi> </mrow> </mrow> <mrow> <mrow> <mi mathvariant="normal">A</mi> </mrow> </mrow> </msub> <mo>-</mo> <mi mathvariant="normal"> </mi> <mn>30</mn> </mrow> </mrow> <mrow> <mrow> <mn>180</mn> <mo>-</mo> <mn>30</mn> </mrow> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mrow> <msub> <mrow> <mrow> <mi mathvariant="normal">t</mi> </mrow> </mrow> <mrow> <mrow> <mi mathvariant="normal">B</mi> </mrow> </mrow> </msub> <mo>-</mo> <mn>0</mn> </mrow> </mrow> <mrow> <mrow> <mn>100</mn> <mo>-</mo> <mn>0</mn> </mrow> </mrow> </mfrac> <mi mathvariant="normal"> </mi> <mi mathvariant="normal"> </mi> </math> </span></div></div><p><span contenteditable="false"> <math> <mfrac> <mrow> <mrow> <msub> <mrow> <mrow> <mi>t</mi> </mrow> </mrow> <mrow> <mrow> <mi>A</mi> </mrow> </mrow> </msub> <mo>-</mo> <mn>30</mn> </mrow> </mrow> <mrow> <mrow> <mn>150</mn> </mrow> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mrow> <msub> <mrow> <mrow> <mi>t</mi> </mrow> </mrow> <mrow> <mrow> <mi>B</mi> </mrow> </mrow> </msub> </mrow> </mrow> <mrow> <mrow> <mn>100</mn> </mrow> </mrow> </mfrac> </math> </span> ,LFP= lower fixed point , UFP= upper fixed point<span contenteditable="false"> <math> <mo>∝</mo> <mi>ρ</mi> </math> </span></p>

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