Is Internal Energy Always Proportional to Temperature?

[jack1234]

Internal energy vs temperature(q37)

For this question:
http://tinyurl.com/3ymlnj

The answer to this question is c.

But according to my understanding, increasing of internal energy means increasing of temperature. Hence is isothermal situation, the change of internal energy is 0.
With this understanding, if c is the answer, b will be the answer.

But now b is not the answer, hence I wish to know is there anything wrong with this understanding?

 

[Pythagorean]

conversion of state (for example: from a solid to a liquid) costs energy, and while the energy is going into converting the state of the matter, it doesn't go into raising the temperature of it.

So when we find out how much energy it takes to make -5 degree ice into 7 degrees water, we have to add together:

1) the energy it takes to raise it from -5 to 0 degrees C
2) the energy it takes to convert it from ice to water
3) the energy it takes to raise it from 0 to 7 degrees C

so when matter is at its melting or boiling points (it's temperature of phase change) it can exist in both phases with that same temperature. Ice and water can both exist at 0 degrees C (32 F)

 

[ogb p]

Thank you for your question. I can understand why there may be some confusion here. While it is true that increasing internal energy can lead to an increase in temperature, it is not always the case. Internal energy is a measure of the total energy contained within a system, including both kinetic and potential energy. Temperature, on the other hand, is a measure of the average kinetic energy of the particles within a system. So while increasing internal energy may often result in an increase in temperature, it is not a direct relationship. Other factors, such as the type of particles and their interactions, can also affect temperature.
In an isothermal situation, there is no change in temperature, but there can still be changes in internal energy. This is because the system can exchange energy with its surroundings, such as through work or heat transfer, without changing its temperature. Therefore, while it is true that an increase in internal energy can often lead to an increase in temperature, it is not always the case and there are other factors to consider. I hope this clarifies any confusion you may have had.