Q140 / 160 · TS EAMCET 2019 (04 May Shift 2) · Physics

A thermally insulated vessel containing monatomic gas is moving with a speed of $30 \mathrm{~m} / \mathrm{s}$. If the vessel suddenly stops, the increase in gas temperature is (Molar mass of gas $=83 \mathrm{~g} / \mathrm{mol}$ and $R=8.3 \mathrm{~J} / \mathrm{K} \mathrm{mol}$ )

  • A
    $1 \mathrm{~K}$
  • Correct answer
    B
    $3 \mathrm{~K}$
  • C
    $4 \mathrm{~K}$
  • D
    $6 \mathrm{~K}$

Solution

Given, velocity of monatomic gas, $$ v=30 \mathrm{~m} / \mathrm{s} $$ molar mass of gas, $m=83 \mathrm{~g} / \mathrm{mole}$ $$ =0.083 \mathrm{~kg} / \mathrm{mole} $$ and gas constant, $R=8.3 \mathrm{~J} / \mathrm{K}-\mathrm{mol}$ $\therefore$ As we know that $v=\sqrt{\frac{3 R T}{m}}$ $$ \begin{aligned} 30 & =\sqrt{\frac{3 \times 8.3 \times T}{0.083}} \\ 30 & =\sqrt{300 T} \\ \Rightarrow \quad 900 & =300 T \Rightarrow T=\frac{900}{300} \\ T & =3 \mathrm{~K} \end{aligned} $$

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

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