A faulty thermometer reads $5^{\circ} \mathrm{C}$ in melting ice and $95^{\circ} \mathrm{C}$ in steam. The correct temperature on absolute scale will be \_\_\_\_ K when the faulty thermometer reads $41^{\circ} \mathrm{C}$.

JEE Main · 2023 · 30 Jan 2023 · Shift 2 · Heat & Thermodynamics

A faulty thermometer reads

5^{\circ} C

in melting ice and

9 5^{\circ} C

in steam. The correct temperature on absolute scale will be ____ K when the faulty thermometer reads

4 1^{\circ} C

Answer: 313

Solution

The faulty scale is linear, reading

5^{\circ}

at the ice point and

9 5^{\circ}

at the steam point, so its

90

divisions correspond to the true interval

0^{\circ}

C to

10 0^{\circ}

\frac{θ _{faulty} - 5}{90} = \frac{θ _{true}}{100}

. A reading of

4 1^{\circ}

gives

θ_{true} = \frac{( 41 - 5 ) \times 100}{90} = 4 0^{\circ}

C, which on the absolute scale is

40 + 273 = 313

JEE Main · 2023 · 30 Jan 2023 · Shift 2 · Integer answer

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