Saved Bookmarks
| 1. |
(i) What are spontaneous reaction? (ii) Prove that for an ideal gas C_(P) is greater than C_(V) |
|
Answer» Solution :(i). A reaction that does occur under the given set of conditions is called a spontaneous reaction. The expansion of a gas into a evauated bulb is a spontaneous process, the reverse process that is gathering of all molecules into one bulb is not spontaneous, This example shows that processes the occur spontaneously in one DIRECTION cannot take place in opposite direction spontaneously. Increase in randomness favours a spontaneous change. If enthalpy change of a process is negative, then the process is EXOTHERMIC and occurs sponteneously. Therefor `DeltaH` should be negative if entropy change of a process is positive, then the process occurs spontaneously, therefore `DeltaS` should be positive. If free energy of a process is negative, then the process occurs sponraneously, `therefore DeltaG` should be negative. For a spontaneous, irreversible process, `DeltaHit0,gt0,DeltaGit0.DeltaH=-ve, DeltaS=+ve and Delta=-ve` . (ii) 1. It is CLEAR that two heat capacities are not EQUAL and `C_(P)` greater than `C_(V)` by a factor which is related to the work done. 2. At a constant pressure, a part of a heat absorbed by the system is used up in increasing the internal energy of the system and the other for doing work by the system. 3. At constant volume the whole of heat absorbed is utlized in increasing the tempreture of the system as there is no work done by the system. Thus `C_(P)` is greater than `C_(V)` `C_(P)=(dH)/(dT), C_(V)=(dU)/(dT)` 4. By defination`H=U+PV` for 1 mole of an ideal gas H=U+RT By diffeentiating this question with repect to tempretureT, we get `(dH)/(dT)=(dU)/(dT)+R C_(P)=C_(V)+R,C_(P)-C_(V)=R` Thus for an ideal gas `C_(P)` is greater than `C_(V)` by the gas constant R. |
|