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  • 3 Moles of a gas mixture having volume  and temperature <img alt="\mathrm{T}" src="https://entran

3 Moles of a gas mixture having volume \mathrm{V} and temperature \mathrm{T} is compressed to 1 / 5 th of the initial volume. Find the change in its adiabatic compressibility if the gas obeys \mathrm{P V^{19 / 3}=constant } \mathrm{[R=8.3 \mathrm{~J} /\mathrm{mol}-\mathrm{K}] }

Option: 1

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Option: 2

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Option: 3

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Option: 4

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Answers (1)

best_answer

\text{Bulk modulus }\mathrm{B}=\gamma \mathrm{P}
\text{Compressibility }\mathrm{C}=\left(\frac{1}{\mathrm{~B}}\right)=\frac{1}{\gamma \mathrm{P}}

\text{and }\quad \Delta \mathrm{C}=\mathrm{C}-\mathrm{C}
or
\mathrm{DC}=\frac{1}{\gamma}\left[\frac{1}{\mathrm{P}^{\prime}}-\frac{1}{\mathrm{P}}\right]
\mathrm{PV}^{\prime}=\mathrm{P}^{\prime}\left(\frac{\mathrm{V}}{5}\right)^{\gamma}

\mathrm{With \gamma=\frac{19}{13}\: and \, \mathrm{P}^{\prime}=5^{\gamma} \mathrm{P}, 11}
\Delta \mathrm{C}=\frac{1}{\gamma \mathrm{P}}\left[\frac{1}{5^{\gamma}}-\frac{1}{1}\right]=\frac{13 \times 0.905}{19 \mathrm{P}}

\text{But }\quad \mathrm{PV}=\mathrm{nRT}$ or $\mathrm{P}=\frac{\mathrm{nRT}}{\mathrm{V}}
\Delta \mathrm{C}=\frac{13 .(0905) \mathrm{V}}{19 \times 3 \times 8.317 \mathrm{~T}}=\frac{-0.0248 \mathrm{~V}}{\mathrm{~T}}

Posted by

Nehul

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