Internal energy (E) is defined as the total energy stored in a system under a given set of conditions. The value of internal energy of a system depends upon such factors as i) the nature of the substance ii) pressure iii) temperature etc. Absolute value of internal energy is impossible to estimate, as the accurate values of different types of energies stored in a system is impossible to quantify precisely. The change in internal energy, ∆E, during a change involving a gaseous system, can be measured from the following relations, which follow from thermodynamic definition of the terms:
q = ∆E + P∆V (at constant pressure)
q = ∆E (at constant volume),
Where, q is the heat change associated with the process, P is the pressure and ∆V, the volume change during the process.
Here, a certain amount of gas is heated at constant volume. Some amount of heat is being put into the system, all of which must be involved in increasing the internal energy of the system. Therefore, the internal energy will increase if the gas is heated and decrease if some heat is extracted from the system, i.e. when the gas is actually cooled.