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  •   Consider two containers A and B containing monoatomic gases at the same Pressure (P), Volume (V) and Temperature (T). The gas  A is compressed isothermally to  <img

 

Consider two containers A and B containing monoatomic gases at the same Pressure (P), Volume (V) and Temperature (T). The gas  A is compressed isothermally to  \frac{1}{8}  of its original volume while the gas in B is compressed adiabatically to  \frac{1}{8}  of its original volume. The ratio of final pressure of gas in B to that of gas in A is

Option: 1

8


Option: 2

4


Option: 3

\frac{1}{8}


Option: 4

8^{\frac{3}{2}}


Answers (1)

best_answer

By Isothermal Process for (A)
\begin{aligned} & P_1 V_1=P_2 V_2 \\ & P V=P_2 \frac{V}{8} \\ & P_2=8 P \end{aligned}
For B adiabatically \gamma_{\text {mono }}=\frac{5}{3}
\begin{aligned} & P_1 V_1^\gamma=P_2 V_2^\gamma \\ & \mathrm{PV}^{5 / 3}=P_2\left(\frac{V}{8}\right)^{5 / 3} \\ & P_2=(8)^{5 / 3} \mathrm{P} \\ & \frac{P_2}{P_1}=\frac{8^{5 / 3}}{8 P}=(8)^{\frac{2}{3}}=4 \end{aligned}
 

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HARSH KANKARIA

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