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`2.8 xx 10^(-2) kg ` of nitrogen is expanded isothermally and reversibly at 300 k from 15.15 `xx 10^(5) Nm^(-2)` when the work done is found to be - 17. 33 kJ .Find the final pressure . |
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Answer» Correct Answer - Final pressure `=1456.8 Nm^(-2)` Given : Mass of nitrogen `= W= 2.8 xx 10^(-2) kg` Temperature = T = 300 K Work obtained in expansion `=W_(max)= - 17 .33 kJ =- 17330 J` Initial pressure `=P_(1) = 15. 15 xx 10^(5) Nm^(-2) = 1.515 xx 10^(6) Nm^(-2)` Molar mass of nitrogen `(N_(2)) = M_(N_(2)) = 28 xx 10^(-3) kg mol^(-1)` Final pressure `= P_(2) = ?` Number of moles of `N_(2) = n. (W)/(M_(N_(2))) = (2.8 xx 10^(-2))/(28xx 10^(-3)) = 1 mol` `W_(max) = - 2.303 xx nRT log _(10) .(P_(1))/(P_(2))` `17330 = 2.303 xx 1 xx 8.314 xx 300 xx log _(10). (1.515 xx 10^(6))/(P_(2))` `:. (17330)/(2.303 xx 1xx 8.314 xx 300) = [ log_(10) 1.515 xx 10^(6) - log_(10) P_(2)]` `3.017 = 6 . 1804 - log _(10) P_(2)` `:. log_(10) P_(2) = 6.1804 - 3.017 =3 . 1634` `:. P_(2) = `Antilog 3.1634 `= 1456.8 Nm^(-2)` |
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