Question

The internal energy and the work done by a system decreases by the same amount then.

Answer 1

Hint: The first law of the thermodynamics has to be concluded from which we can know that the change in internal energy of any system is the sum of the work done and heat exchange. When work is done by a system it loses energy and hence taken as negative. Due to negative work done the equation can be changed. We have show here what happens if the work done becomes more than the amount of heat.

Complete answer:
From, the first law of thermodynamics described that the change in internal energy \[\Delta U\] of a closed system is equal to the heat added to the system (\[Q\]) minus the work done by the system (\[W\]).
\[\Delta U{\text{ }} = {\text{ }}Q{\text{ }} - {\text{ }}W\]
So if the internal energy decreases, we can conclude that the quantity \[Q{\text{ }} - {\text{ }}W\] is negative, therefore \[W\] \[ \geqslant \] \[Q\] meaning the system did more work (perhaps by displacing its environment in the form of $\left( {PdV} \right)$ work) than the amount of heat that may have been added to the system.
If the system was kept at a constant volume, then there is no displacement work could be done and the only way the system could experience a decrease in internal energy
The Sum of the work done and heat exchange gives the Change in internal energy.
 If the process has no heat exchange which is referred to as adiabatic and hence temperature gets decreases.

Note:
The system's internal energy decreases. When a system has work done on it
When there is no exchange of heat takes place is called the adiabatic process
The change in internal energy of a gas is equal to work done by the gas which is known as the adiabatic process.