Q138 / 160 · TS EAMCET 2021 (05 Aug Shift 1) · Physics

An ideal gas undergoes an adiabatic process. If the pressure of the gas is reduced by $0.1 %$ then the volume is changed by (Given $r = \frac{C_{p}}{C_{v}} = \frac{5}{3}$ )

Solution

The relation between pressure and volume in the case of the adiabatic process,

P V^{γ} = K

, now for two different conditions,

P_{1} {V_{1}}^{γ} = P_{2} {V_{2}}^{γ}

, here

P_{2} = \frac{P_{1} \times 0.1}{100}

, put the values in the above expression,

\frac{P_{1} \times 100}{P_{1} \times 0.1} = {(\frac{V_{2}}{V_{1}})}^{\frac{5}{3}} \Rightarrow {(\frac{V_{2}}{V_{1}})}^{\frac{5}{3}} = 1000 \Rightarrow \frac{V_{2}}{V_{1}} = {(1000)}^{\frac{3}{5}} \Rightarrow V_{2} = 0.6 % V_{1}

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