Should there also be an assumption for ideal gaes that states: The gas molecules/atoms do not vibrate and rotate I was considering a case of a gas expanding at a dropping pressure such that the value of PV remains a constant. Work is done since there is an increase in volume. If there is no heat transfer into a system, from the first law of thermodynamics Q=W+(delta)U The change in internal energy should be equals to the negative of the work done by the gas. But the temperature remains unchanged, thus the internal energy of the gas does not change. Now we have 2 conflicting results that can only mean thermal energy must be transferred into the system for the above example to occur. But we know that in reality, the vibrations and rotational movement of the gas molecules can account for the drop in internal energy, but since the internal energy is a function of temperature and temperature is a function of the average translational kinetic energy of the gas molecules, should there not be a new assumption that states that ideal gas molecules does not rotate and vibrate? In short my question really is, since internal energy is a function of the average translational kinetic energy of the gas molecules, this should be made applicable only to ideal gases since in reality, the internal energy can and should cover the rotational and vibration motion of these molecules.