Question

The internal energy and the work done by a system decrease by the same amount then?

Answer 1

Adiabatic process:

1. The process is generally said to be an adiabatic process if no heat enters and leaves the system during any stage of the process.
2. Let the system absorb the heat ‘q’ from the surroundings and perform the work which tends to lower the energy of the system.
3. As the performance of the work requires the expenditure of energy, hence, the change of internal energy $\mathrm{\Delta }\text{U}$ can be given by:
   $\mathrm{\Delta }\text{U = q + w}$
4. Here$\mathrm{\Delta }\text{U}$ the internal energy and q is termed as the heat transferred from the surroundings to the system and w is the work done.
5. The condition in which the internal energy of the system decreases to reach the value of work, here the internal energy is equal to the work done by the system.
6. That is, at a certain condition the internal energy and work done become equal, hence the above equation can be given as:
   $\begin{array}{rl}& \mathrm{\Delta }\text{U = q + w}\\ & \Rightarrow \text{w = q + w}\\ & \Rightarrow \text{q = w}-\text{w}\\ & \therefore \text{q = 0}\end{array}$
7. When the internal energy of an ideal gas decreases by the same amount as the work done by the system, then $\text{q = 0}$.
8. A process in which no heat enters or leaves the system is known as the adiabatic process.

Hence, no heat is allowed to enter or leave the system, the above process is adiabatic.