Consider two containers A and B containing monoatomic gases at the same Pressure P , Volume V and Temperature T . The gas in A is compressed isothermally to 1 8 of its original volume while the gas in

Question

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

TestHub · Accepted Answer

In an isothermal process the temperature is constant.
$P V = n R T$
So, it can be written that
$P V = P_{A} (\frac{V}{8}) \Rightarrow P_{A} = 8 P$
In an adiabatic process,
$P V^{γ} =$ constant
$γ$ for monoatomic gas is $\frac{5}{3}$
So, it can be written
$\frac{P_{B}}{P} = {(\frac{V}{\frac{V}{8}})}^{\frac{5}{3}} \Rightarrow P_{B} = 32 P$
Thus, the ratio of the pressures is
$\frac{P_{B}}{P_{A}} = \frac{32 P}{8 P} = 4$

Physics - Heat & Thermo Question with Solution | TestHub

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