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11. thermodynamics — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics11. thermodynamics1 Mark
MCQ
In a certain thermodynamical process, the pressure of a gas depends on its volume as $kV ^{3}$. The work done when the temperature changes from $100^{\circ} C$ to $300^{\circ} C$ will be .......... $nR$, where $n$ denotes number of moles of a gas.
  • A
    $25$
  • B
    $40$
  • ✓
    $50$
  • D
    $60$
✓

Answer

Correct option: C.
$50$
c
$P=k V^{3}$

$T_{i}=100^{\circ} C $

$T _{ f }=300^{\circ} C$

$\Delta T =300-100$

$\Delta T =200^{\circ} C$

$P = kV ^{3}$

now $PV = nRT$

$\therefore kV ^{4}= nRT$

now $4 kV ^{3} dV = nRdT$

$\therefore PdV = nRdT / 4$

$\therefore$ Work $=\int PdV =\int \frac{ nRdT }{4}=\frac{ nR }{4} \Delta T$

$=\frac{200}{4} \times nR =50 nR$

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