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10-1.Thermometry, Thermal Expansion and Calorimetry
normal
A constant volume gas thermometer shows pressure reading of $50 \,cm$ and $90 \,cm$ of mercury at $0^{\circ} C$ and $100^{\circ} C$ respectively. When the pressure reading is $60 \,cm$ of mercury, the temperature is ......... $^{\circ} C$
A
$25$
B
$40$
C
$15$
D
$12.5$
Solution
(a)
$T _0=0^{\circ}\,C , T _1=100^{\circ}\, C , h_0=50\, cm$
and $h _1=90\,cm$
Rate of change in height wrt $T =\frac{ h _1- h _0}{ T _1- T _0}$
$\frac{\Delta h }{\Delta t }=\frac{40}{100}$
for height $(h)=60\, cm$, let the
corresponding temperature be $T$.
Then $\,\frac{ h – h _0}{ T – T _0}=\frac{\Delta h }{\Delta t }=\frac{40}{100}$
$\Rightarrow \frac{60-50}{T-0^{\circ} C }=\frac{4}{10}$
$\Rightarrow \frac{10 \times 10}{4}= T \Rightarrow T =25^{\circ}\,C$
Standard 11
Physics
