The resistance of the platinum wire of a platinum resistance thermometer at the ice point is \( 5\,\Omega \) and at steam point, it is \( 5.23\,\Omega \). When the thermometer is inserted in a hot bath, the resistance of the platinum wire becomes \( 5.795\,\Omega \). Find the temperature of the bath.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( 345.65^\circ\mathrm{C} \)
A platinum resistance thermometer uses the linear variation of resistance with temperature, \( R_t = R_0(1 + \alpha t) \). Between the ice point (\( 0^\circ\mathrm{C} \)) and the steam point (\( 100^\circ\mathrm{C} \)) the rise in resistance is \( R_0\alpha \times 100 \), so
\( \displaystyle t = \frac{R_t - R_0}{R_{100} - R_0}\times 100^\circ\mathrm{C} \)
\( R_0 = 5\,\Omega \)
\( R_{100} = 5.23\,\Omega \)
\( R_t = 5.795\,\Omega \)
\( \displaystyle t = \frac{5.795 - 5}{5.23 - 5}\times 100 = \frac{0.795}{0.23}\times 100 = 345.65^\circ\mathrm{C} \)
Note: This question is from NCERT (2026-27). NTA sets numerical questions from NCERT too, so do not ignore NCERT while practising numericals.
NCERT (2026-27):
Temperature Dependence of Resistivity – …
