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11. thermodynamics — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics11. thermodynamics1 Mark
MCQ
$5.6$ $liter$ of helium gas at $STP$ is adiabatically compressed to $0.7$ $liter$. Taking the initial temperature to be $T_1$, the work done in the process is
  • ✓
    $\frac{9}{8}$$RT_1$
  • B
    $\frac{3}{2}$$RT_1$
  • C
    $\frac{15}{8}$$RT_1$
  • D
    $\frac{9}{2}$$RT_1$
✓

Answer

Correct option: A.
$\frac{9}{8}$$RT_1$
a
No. of moles $=n=\frac{5.6}{22.4}=\frac{1}{4}$

$\mathrm{TV}^{\gamma -1}=$ constant $\Rightarrow \mathrm{T}_{1}(5.6)^{2 / 3}=\mathrm{T}_{2}(0.7)^{2 / 3}$

$\Rightarrow \mathrm{T}_{1}(8)^{2 / 3}=\mathrm{T}_{2} \Rightarrow 4 \mathrm{T}_{1}=\mathrm{T}_{2}$

$\mathrm{W}_{\mathrm{gas}}=\frac{-n R \Delta T}{\gamma-1}=-\frac{(1) R\left(3 T_{1}\right) \times 3}{4 \times 2}=-\frac{9}{8} R T_{1}$

Therefore $\mathrm{W}_{\text {external}}=\frac{9}{8} R T_{1}$

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