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  • When an ideal gas at pressure P, temperature T and volume V is isothermally compressed to a <img alt="\mathrm{V / n}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7BV%20/%20n%7D"

When an ideal gas at pressure P, temperature T and volume V is isothermally compressed to a \mathrm{V / n}, its pressure becomes \mathrm{P_{i}}.If the gas is compressed adiabatically to \mathrm{V} / \mathrm{n},  its pressure becomes \mathrm{P}_{\mathrm{a}}.The ratio \mathrm{P}_{\mathrm{i}} / \mathrm{Pa} is

Option: 1

1


Option: 2

\mathrm{n}


Option: 3

\mathrm{n^{r}}


Option: 4

\mathrm{n^{1-\gamma }}


Answers (1)

best_answer

For isothermal process, \mathrm{PV}= constant. Therefore

\mathrm{P}_{\mathrm{i}} \mathrm{V}_{\mathrm{i}}=\mathrm{PV} \text { or } \mathrm{P}_{\mathrm{i}} \frac{V}{n}=P V \text { or } \mathrm{P}_{\mathrm{i}}=\mathrm{nP}\quad \ldots(i)

For adiabatic process, \mathrm{PV_{\gamma=}} constant. Therefore

\mathrm{Pa}(\mathrm{Va})^{\gamma}=\mathrm{PV}^{\gamma}
P_{a}\left(\frac{V}{n}\right)^{\gamma}=P V^{\gamma}

\text { or } \quad \mathrm{Pa}_{\mathrm{a}}=\mathrm{n}^{\gamma} \mathrm{P}\quad \ldots(ii)

 From (i) and (ii) we get
\mathrm{ \frac{P_{i}}{P_{a}}=\frac{n}{n^{\gamma}}=n^{(1-\gamma)}}

 

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avinash.dongre

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