# Change in internal energy if temperature is constant and some moles of the gas dissociate

"Change in internal energy is zero if temperature is constant because, internal energy is a function of temperature only." Well, this is what I read everytime I study thermodynamics. I came across a question where some heat (Q) was provided and due this heat supplied, a few moles of the gas dissociate. But, in this process, the temperature remains constant. If temperature is constant, change in internal energy should be zero. But, does this rule work even if some molecules dissociate? Will the internal energy change(although the temperature is constant) due to dissociation?

Change in internal energy is zero if temperature is constant because, internal energy is a function of temperature only

This true for an ideal gas, but not true for real gases where we get interactions between the gas particles. The obvious example of this is the Joule expansion. In this process no energy is added an now work is done so the internal energy remains constant. For an ideal gas the temperature does remain constant, but for real gases the temperature can increase or decrease depending on how the gas atoms/molecules interact with each other.

Your example of a dissociating molecule is basically an extension of this where the forces between the gas particles are strong enough to bind them into molecules.

In a Joule expansion some of the gas particles' kinetic energy is converted to potential energy or vice versa. The internal energy is the sum of the kinetic and potential energy while the temperature depends only on the kinetic energy. That's why when when the potential energy is significant the internal energy and the temperature are not simply proportional.

In the specific case of your dissociating molecule, we have to put work in to separate the parts of the molecule from the force binding them together, so the potential energy increases. The heat supplied to the system is going into the increase in the potential energy and leaving the kinetic energy unchanged. So the internal energy is increasing while the kinetic energy, and therefore the temperature, is not changed.

• Due to dissociation, there is an increase in the KINETIC energy, right? So, the temperature will increase which is not get the case here.. Why did you say that POTENTIAL ENERGY increases? Commented Dec 16, 2017 at 7:52
• @user166465 Where did I say the potential energy increases? Commented Dec 16, 2017 at 7:55
• Well sorry. U said potential energy significant. I didn't get the potential energy part. Like, kinetic energy increases due to dissociation right? So why does the temperature not increase?? Commented Dec 16, 2017 at 7:58
• @user166465 if you take the example of a dissociating molecule then when the molecules dissociate the potential energy increases because we are separating the parts of the molecule against the force binding them together. If we don't add any energy then because the internal energy is constant the kinetic energy must decrease so the gas gets colder . So we have to add heat to bring the temperature back to its original value. That's why in your example we add heat but the temperature stays constant. Commented Dec 16, 2017 at 8:03
• Okayy!!! So, though the temperature is constant, potential energy is increasing and hence there is an increase in internal energy right?! Commented Dec 16, 2017 at 8:04