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Thermodynamics — Physics STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 SciencePhysicsThermodynamics3 Marks
Question
A gas with adiabatic constant $\gamma=1.4$, expands adiabatically so that the final pressure becomes half the initial pressure. If the initial volume of the gas $1 \times 10^{-2} m ^3$, find the final volume.
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Answer

$ \text { Data : } \gamma=1.4, P_{ f }=0.5 P_{ i }, V_{ i }=1 \times 10^{-2} m ^3$
$P_{ i } V_{ i }^\gamma=P_{ f } V_{ f }^\gamma \quad \therefore\left(\frac{V_{ f }}{V_{ i }}\right)^\gamma=\frac{P_{ i }}{P_{ f }}=2$
$\therefore \gamma \log \left(\frac{V_{ f }}{V_{ i }}\right)=\log 2 \quad \therefore \log \left(\frac{V_{ f }}{V_{ i }}\right)=\frac{\log 2}{\gamma}=$
$\frac{0.3010}{1.4}=0.215$
$\therefore \frac{V_{ f }}{V_{ i }}=\text { antilog } 0.215=1.641$
$\therefore V_{ f }=1.641 V_{ i }=(1.641)\left(1 \times 10^{-2}\right) m ^3$
$=1.641 \times 10^{-2} m ^3 $
This is the final volume of the gas.

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