One mole of an ideal gas undergoes reversible isothermal expansion from an initial volume ofV_(1) to a final volume of 10V_(1) and does 10kJof work. The initial pressure was 1xx 10^(7) Pa. (a) Calculate V_(1). (b) If there were 2 moles of gas, what must its temperature have been ?

One mole of an ideal gas undergoes reversible isothermal expansion fro

1.	One mole of an ideal gas undergoes reversible isothermal expansion from an initial volume ofV_(1) to a final volume of 10V_(1) and does 10kJof work. The initial pressure was 1xx 10^(7) Pa. (a) Calculate V_(1). (b) If there were 2 moles of gas, what must its temperature have been ?
Answer» Solution :(a) `w = 2.303nRT log. (V_(2))/(V_(1))` `10 xx 10^(3) J= 2.303 xx 1 xx 8.314 xx T xx log . ( 10V_(1))/( V_(1))` or`T = 522.3 K` For initial conditions, ` P_(1)V_(1) = n_(1)RT` i.e., `( 10^(7)Pa) V_91) = 1 xx 8.314 xx 522.3` or ` V_(1) = 4.342 xx 10^(-4) m^(3) = 4.342 xx 10^(2) CM^(3) =434 .2 cm^(3)` Note. We cannot apply the formula `-x = P Delta V` because expansion is not against constant PRESSURE. (B) If there were 2 moles of the gas, applying `P_(1)V_91) = n_(1)RT ` , we GET `( 10^(7) Pa) ( 4.342 xx 10^(-4)m^(3)) =2 xx 8.314 xx T` or`T = 261.1 K`, i.e. half of the first value