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11. thermodynamics — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics11. thermodynamics1 Mark
MCQ
A sample of gas at temperature $T$ is adiabatically expanded to double its volume. The work done by the gas in the process is $\left(\right.$ given, $\left.\gamma=\frac{3}{2}\right)$ :
  • A
    $W=T R[\sqrt{2}-2]$
  • B
    $W=\frac{T}{R}[\sqrt{2}-2]$
  • C
    $W=\frac{R}{T}[2-\sqrt{2}]$
  • ✓
    $W=R T[2-\sqrt{2}]$
✓

Answer

Correct option: D.
$W=R T[2-\sqrt{2}]$
d
$T_1 V_1^{\gamma-1}=T_2 V_2^{\gamma-1}$

$T V^{1 / 2}=T_2(2 V)^{1 / 2}$

$T_2=\frac{T}{\sqrt{2}}$

$W=\frac{R\left(T_1-T_2\right)}{\gamma-1}=\frac{R\left(T-\frac{T}{\sqrt{2}}\right)}{\frac{1}{2}}=R T(2-\sqrt{2})$

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