Q160 / 200 · Manipal (MET) 2012 · Physics

If pressure of a gas contained in a closed vessel is increased by $0.4 \%$ when heated by $1^{\circ} \mathrm{C}$, its initial temperature must be

  • Correct answer
    A
    250 K
  • B
    $250^{\circ} \mathrm{C}$
  • C
    $25^{\circ} \mathrm{C}$
  • D
    2500 K

Solution

\(\begin{aligned} & \frac{\mathrm{pV}}{\mathrm{~T}}=\text { constant; } \mathrm{V}=\text { constant } \\ & \therefore \frac{\mathrm{p}}{\mathrm{~T}}=\text { constant } \\ & \therefore \frac{\mathrm{p}}{\mathrm{~T}}=\frac{100.4 \mathrm{p}}{1000} \cdot \frac{1}{(\mathrm{~T}+1)} \\ & \frac{1}{\mathrm{~T}}=\frac{100.4}{100} \cdot \frac{1}{(\mathrm{~T}+1)} \\ & \frac{1}{\mathrm{~T}}=\frac{100.4}{100 \mathrm{~T}+100} \\ & \mathrm{~T}=250 \mathrm{~K} \end{aligned}\)

Hence, the correct answer is option: 'A'.

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