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11. thermodynamics — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics11. thermodynamics1 Mark
MCQ
Neon gas of a given mass expands isothermally to double volume. What should be the further fractional decrease in pressure, so that the gas when adiabatically compressed from that state, reaches the original state?
  • ✓
    $1-2^{-2 / 3}$
  • B
    $1-3^{1 / 3}$
  • C
    $2^{1 / 3}$
  • D
    $3^{2 / 3}$
✓

Answer

Correct option: A.
$1-2^{-2 / 3}$
a
(a)

$P_1 V_1=P_2 V_2$   [for isothermal]

$P V=P \times 2 V$

$\frac{P}{2}=P^{\prime}$

$P_1 V_1^\gamma=P_2 V_2^\gamma$   [for adiabatic]

$\frac{P}{2} \times(2 V)^{5 / 3}=P_2(V)^{5 / 3}$    $[\gamma$ for neon $=5 / 3]$

$P=P_2 \cdot(2)^{-2 / 3}$

Fractional decrease $=\frac{P_2-P}{P_2}=\frac{P_2-P_2 \cdot(2)^{-2 / 3}}{P_2}=1-2^{-2 / 3}$

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