InterviewSolution
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InterviewSolution
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Write expression for the work done by 1 mole of the gas in each of the following cases `:` (i) For irreversible expansion of the gas from volume `V_(1)` to `V_(2)`. (ii) For reversible isothermal expansion of the gas from volume `V_(1)` to`V_(2)`. (iii)For expansion of the gas into an evaluated vessel. (iv) For reversible isothermal compression of the gas from pressure `P_(1)` to `P_(2)` (v)For adiabatic expansion resulting into change of temperature from `T_(1)` to `T_(2)`. |
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Answer» (i)Irreversible expansion takes place when external pressure `(P_(ext))` remains constant `w_("irrev")= - P_("ext") (V_(2)-V_(1))= -P_(ext) DeltaV` (ii) Reversible expansion takes place when internal pressure is infinitesimally greater than exterhanl pressure `(P_("int")~=P_(ext))` at every stage. Thsu, externalpressurehas to be adjusted throughout. `w_(rev)= -nRT ln. (V_(2))/(V_(1))` (iii) The expansion is irreversible. Further, as `P_(ext) =0`, therefore, `w= -P_(ext)DeltaV= 0 xx ( DeltaV) = 0` (iv) When gas is compressed, work is done on the gas. For isothermal reversible compression, `w= + nRT ln. (P_(2))/(P_(1))` (v) For adiabatic expansion, temperature falls, i.e.,`T_(2) ltT_(1))` `w=C_(v) (T_(2)-T_(1)),i.e., w` is -ve. |
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