Q171 / 200 · Manipal (MET) 2010 · Physics

A gas is suddenly expanded such that its final volume becomes 3 times its initial volume. If the specific heat at constant volume of the gas is $2 R$, then the ratio of initial to final pressures is nearly equal to

  • Correct answer
    A
    $5$
  • B
    $6.5$
  • C
    $7$
  • D
    $3.5$

Solution

As gas is suddenly expanded so it is an adiabatic process, ie, $p V^\gamma=$ constant Given $V_2=3 V_1, C_V=2 R$ $\begin{array}{ll}\therefore & C_p=2 R+R=3 R \\ \Rightarrow & \gamma=\frac{C_p}{C_V}=\frac{3 R}{2 R}=1.5\end{array}$ $\therefore \frac{p_1}{p_2}=\left(\frac{V_2}{V_1}\right)^\gamma=(3)^{1.5}=5.1 \approx 5$

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

Relevant Questions