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11. thermodynamics — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics11. thermodynamics1 Mark
MCQ
An ideal gas is taken through a quasi-static process described by $P = \alpha\, V^2$, with  $\alpha = 5\,atm/m^6$. The gas is expanded to twice its original volume of $1\,m^3$. How much work is done by the expanding gas in this process
  • A
    $10.8\,J$
  • ✓
    $1.18\,M\,J$
  • C
    $5\,J$
  • D
    $4.3\,M\,J$
✓

Answer

Correct option: B.
$1.18\,M\,J$
b
$\mathrm{W}=\int_{\mathrm{V}_{1}}^{\mathrm{v}_{2}} \mathrm{P} \mathrm{d} \mathrm{v}$

$=5 \times 10^{5} \int_{1}^{2} \mathrm{V}^{2} \mathrm{d} \mathrm{v}$

$=5 \times 10^{5}\left[\frac{V^{3}}{3}\right]_{1}^{2}$

$=\frac{5}{3} \times\left[2^{3}-1^{3}\right] \times 10^{5} \mathrm{J}$

$=1018 \mathrm{MJ}$

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